Safety Factor Approach Research Articles

Comparative study of deterministic and probabilistic critical slip surfaces applied to slope stability using limit equilibrium methods and the First-Order Reliability Method

This work presents the validation of the Morgenstern-Price method implemented in the Risk Assessment applied to Slope Stability (RASS) computational program to carry out deterministic and probabilistic analyses of slope stability. Deterministic analyses, based on the factor of safety approach, are performed using limit equilibrium methods. The probabilistic ones, on the other hand, are carried out through the direct coupling of these methods to the First Order Reliability Method (FORM). Initially, two benchmark cases are presented for validation of the computational routine related to the Morgenstern-Price method. Next, two illustrative examples are presented, with the investigation of the critical surfaces defined by deterministic and probabilistic criteria, which correspond to the minimum factor of safety, the maximum probability of failure, and the maximum quantitative risk. In the set of stability analyses, it was verified that both the numerical responses and the geometry of the critical surfaces can vary depending on the choice of the limit equilibrium method and the criterion for identifying the critical surface. The different possibilities presented by the methodology used in this study define not only a critical surface, but a set of critical surfaces that can help in the engineering decision-making process and slope risk management, complementing the widely used purely deterministic analyses in geotechnics.

Reverse optimum safety factor approaches as effective tools for reliability-based topology optimization with application to cementless hollow stems used in total hip replacement

Reverse optimum safety factor approaches as effective tools for reliability-based topology optimization with application to cementless hollow stems used in total hip replacement

Reverse Versus Inverse Optimum Safety Factor Approaches for Reliability-based Topology Optimization

Reverse Versus Inverse Optimum Safety Factor Approaches for Reliability-based Topology Optimization

Reliability-Based Robust Design of Raft Foundation and Effect of Spatial Variability

Geotechnical design considers different limit states of design. Conventional deterministic design methodology uses the factor of safety approach, while reliability-based design and robust design methodology use probability distribution and statistics of properties. In this study, different design methodologies were compared. Efficient probabilistic methods and optimization techniques such as the first-order reliability method and genetic algorithm were used to arrive at a robust and optimized design. Estimation of system reliability helps in attributing importance to both the limit states involved, simultaneously. In addition, a combination of random field theory with numerical modeling in the framework of the Monte Carlo simulation method and response surface method was used in considering spatial variability. In this way, the risk involved while using conventional deterministic design methodology is brought out; it is apparent from the larger foundation sizes obtained using reliability-based and robust design methodologies. This emphasizes the importance of considering the variability of soil and the robustness of design for critical structures using probabilistic methods.

A Safety Factor Approach to Designing Urban Infrastructure for Dynamic Conditions

AbstractCurrent approaches to design flood‐sensitive infrastructure typically assume a stationary rainfall distribution and neglect many uncertainties. These assumptions are inconsistent with observations that suggest intensifying extreme precipitation events and the uncertainties surrounding projections of the coupled natural‐human systems. Here we demonstrate a safety factor approach to designing urban infrastructure in a changing climate. Our results show that assuming climate stationarity and neglecting deep uncertainties can drastically underestimate flood risks and lead to poor infrastructure design choices. We find that climate uncertainty dominates the socioeconomic and engineering uncertainties that impact the hydraulic reliability in stormwater drainage systems. We quantify the upfront costs needed to achieve higher hydraulic reliability and robustness against the deep uncertainties surrounding projections of rainfall, surface runoff characteristics, and infrastructure lifetime. Depending on the location, we find that adding safety factors of 1.4–1.7 to the standard stormwater pipe design guidance produces robust performance to the considered deep uncertainties. The insights gained from this study highlights the need for updating traditional engineering design strategies to improve infrastructure reliability under socioeconomic and environmental changes.

Sliding stability analyses of a rock slope using deterministic, semi-probabilistic and probabilistic methods

Stability analyses of geotechnical structures in rock are traditionally performed using deterministic methods. In Europe, Eurocode7, introduced in the beginning of the 21st century, adopts limit state design and semi-probabilistic methods, using partial factors for the design of geotechnical structures. Meanwhile, reliability-based design, using probabilistic methods, is becoming more common in practical cases. The paper considers an intentionally simple case study—the analysis of a slope in a rock mass with one discontinuity, considered in a discrete way, forming a rock block to be stabilised by anchors—to compare the results obtained with the different methods. The objective is to calculate the force applied by the anchors so that the ultimate limit states of sliding of the rock block is verified. Deterministic-based design optimization considering both the traditional global safety factor approach and the partial factor approach following the Eurocode 7 are first applied. A reliability-based design optimization procedure—which takes geometrical and mechanical properties of the discontinuities as random variables—is then used, and the results are compared to the former ones. A discussion is presented concerning the consistency of the obtained results.

Monitoring and Mapping of Shallow Landslides in a Tropical Environment Using Persistent Scatterer Interferometry: A Case Study from the Western Ghats, India

Persistent Scatterer Interferometry (PSI) techniques are now well established and accepted for monitoring ground displacements. The presence of shallow-seated landslides, ubiquitous phenomena in the tropics, offers an opportunity to monitor and map these hazards using PSI at the regional scale. Thus, the Western Ghats of India, experiencing a tropical climate and in a topographically complex region of the world, provides an ideal study site to test the efficacy of landslide detection with PSI. The biggest challenge in using the PSI technique in tropical regions is the additional noise in data due to vegetation. In this study, we filtered these noises by utilizing the 95-percentile of the highest coherence data, which also reduced the redundancy of the PSI points. The study examined 12 landslides that occurred within one of the three temporal categories grouped as Group 1, Group 2, and Group 3, categorized in relation to PSI monitoring periods, which was also further classified into east- and west-facing landslides. The Synthetic Aperture Radar (SAR) data is in descending mode, and, therefore, the east-facing landslides are characterized by positive deformation velocity values, whereas the west-facing landslides have negative deformation values. Further, the landslide-prone areas, delineated using the conventional factor of safety (FS), were refined and mapped using PSI velocity values. The combination of PSI with the conventional FS approach helped to identify exclusive zones prone to landslides. The main aim of such an attempt is to identify critical areas in the unstable category in the map prepared using FS and prioritizing the mitigation measures, and to develop a road map for any developmental activities. The approach also helps to increase confidence in the susceptibility mapping and reduce false alarms.

Calibration of Load and Resistance Factors of API RP 2A-LRFD, Second Edition, for Fixed Offshore Platforms

AbstractFixed offshore platforms in the Gulf of Mexico (GoM) are traditionally designed following the working stress design (WSD) format, that is, the factor of safety approach. In 1993, the first ...

An efficient reliability-based design optimization study for PCM-based heat-sink used for cooling electronic devices

Nowadays, development of new technologies requires efficient mechatronic components which needs more sophisticated cooling systems. Furthermore, phase change material (PCM) based heat sinks presents an appropriate technique for electronic devices. Then, the aim of this work is to propose an efficient methodology that determines an optimal design of such a PCM-based cooling system. Despite of the satisfaction of the optimal solution founded by the deterministic design optimization (DDO), the reliability level is not controlled. For this reason, reliability-based design optimization (RBDO) studies were performed. In fact, RBDO approaches aim to find the best compromise between safety and cost by taking into consideration uncertainties for the studied model. Therefore, several methods are studied, such as the optimum safety factor approach and the hybrid method. Yet, the application of these methods is limited only to linear materials. Hence, this study presents an extension in the case of nonlinear materials. In addition, to overcome problems of the classical hybrid approach, a Robust Hybrid Method (RHM) is proposed. A numerical application is used to study the different DDO and RBDO methods. Then, the efficiency of the RHM method for PCM-based heat sinks is verified.

Reliability-Based Topology Optimization Using Two Alternative Inverse Optimum Safety Factor Approaches: Application to Bridge Structures

Introduction. The Deterministic Topology Optimization model provides a single solution for a given design space, while the Reliability-Based Topology Optimization model provides several reliability-based topology layouts with high-performance levels. The objective of this work is to develop two strategies that can provide the designer with two categories of resulting topologies. Materials and Methods. Two alternative approaches based on the Inverse Optimum Safety Factor are developed: the first one is called the Objective-Based IOSF Approach and the second one is called Performance-Based IOSF Approach. When dealing with bridge structures, the uncertainty on the input parameters (boundary conditions, material properties, geometry, etc.) and also output parameters (compliance, etc.) should not be ignored. The sensitivity analysis is the fundamental idea of both developed approaches, identifies the role of each parameter on the structural performance. In addition, the optimization domain choice is important when eliminating material that should not affect the structure functioning. Results. Two numerical examples on a 2D bridge structure are presented to demonstrate the efficiency of the developed approaches. When considering a certain reliability level, the Reliability-Based Topology Optimization leads to two different configurations relative to the Deterministic Topology Optimization one. When increasing the reliability levels, the quantity of materials decreases that leads to an increase in the number of holes in the structures. Discussion and Conclusion. In addition to their simplified implementation, the developed alternative approaches can be considered as two generative tools to produce two different categories (families) of solutions where an alternative choice between two functions (objective/performance) is presented.

Reliability-based topology optimization using inverse optimum safety factor approaches

The Deterministic Topology Optimization (DTO) model generates a single solution for a given design space, while the Reliability-Based Topology Optimization (RBTO) model provides several reliability-based topology layouts with high performance levels. The objective of this work is to develop two approaches, which can lead to two new topology categories. The two alternative approaches; namely Objective-Based Inverse Optimum Safety Factor (IOSF) and Performance-Based IOSF, are developed based on the IOSF. When designing a structure, the uncertainty in the input parameters influences the output parameters and thus a sensitivity analysis was carried out for the developed approaches. The analysis shows the influence of each parameter on the structure performance. Two numerical applications are presented to show the effectiveness of the developed approaches. When considering a certain reliability level, unlike the DTO, the RBTO results in different configurations. Unlike the results of the previous studies, the consideration of the geometry uncertainty reveals that the structural volume increases as the reliability level increases. Additionally, the developed approaches can be considered as two generative tools that can produce two different categories/families of solutions.

Predicting Hard Rock Pillar Stability Using GBDT, XGBoost, and LightGBM Algorithms

Predicting pillar stability is a vital task in hard rock mines as pillar instability can cause large-scale collapse hazards. However, it is challenging because the pillar stability is affected by many factors. With the accumulation of pillar stability cases, machine learning (ML) has shown great potential to predict pillar stability. This study aims to predict hard rock pillar stability using gradient boosting decision tree (GBDT), extreme gradient boosting (XGBoost), and light gradient boosting machine (LightGBM) algorithms. First, 236 cases with five indicators were collected from seven hard rock mines. Afterwards, the hyperparameters of each model were tuned using a five-fold cross validation (CV) approach. Based on the optimal hyperparameters configuration, prediction models were constructed using training set (70% of the data). Finally, the test set (30% of the data) was adopted to evaluate the performance of each model. The precision, recall, and F1 indexes were utilized to analyze prediction results of each level, and the accuracy and their macro average values were used to assess the overall prediction performance. Based on the sensitivity analysis of indicators, the relative importance of each indicator was obtained. In addition, the safety factor approach and other ML algorithms were adopted as comparisons. The results showed that GBDT, XGBoost, and LightGBM algorithms achieved a better comprehensive performance, and their prediction accuracies were 0.8310, 0.8310, and 0.8169, respectively. The average pillar stress and ratio of pillar width to pillar height had the most important influences on prediction results. The proposed methodology can provide a reliable reference for pillar design and stability risk management.

Reliability-based design optimization for heat flux analysis of composite modular walls using inverse reliability assessment method

Abstract Modular composite walls are widely used in many industrial applications such as thermal applications, different kinds of heat exchangers … etc. These structures allow to rapidly and economically divide spaces and to create separate areas. Different size and shape of a wall can be combined and connected to build permanent or temporary walls that meet a space's specific needs. The integration of reliability and optimization concepts into the modular composite wall design seeks to provide structures that should be both economic and reliable. This model is called Reliability-Based Design Optimization (RBDO). In fact, the classical coupling between the numerical modeling, the reliability analyses and the optimization methods leads to a high computational cost and weak convergence stability. To overcome these difficulties, several developments have been carried out during the last three decades. Some of these approaches treat the convergence stability such the hybrid approaches and the others treat the computing time problem such optimum safety factor approaches. In this paper, a new method called Inverse Reliability Assessment Method (IRAM) is proposed to deal with a single type of variables for the studied optimization problem. It consists of performing the optimization process to find the Failure Point (FP) and next an inverse assessment of the reliability level is carried out to find the RBDO solution. A numerical application on the heat flux analysis is carried out using two computational procedures on two different cases of a composite modular walls. The first procedure is to assess the reliability level of the given point and the second one is to improve the resulting values, through the RBDO using the proposed method (IRAM).

Efficient optimum safety factor approach for system reliability-based design optimization with application to composite yarns

Introduction. The integration of reliability and optimization concepts seeks to design structures that should be both economic and reliable. This model is called Reliability-Based Design Optimization (RBDO). In fact, the coupling between the mechanical modelling, the reliability analyses and the optimization methods leads to very high computational cost and weak convergence stability. Materials andMethods. Several methods have been developed to overcome these difficulties. The methods called Reliability Index Approach (RIA) and Performance Measure Approach (PMA) are two alternative methods. RIA describes the probabilistic constraint as a reliability index while PMA was proposed by converting the probability measure to a performance measure. An Optimum Safety Factor (OSF) method is proposed to compute safety factors satisfying a required reliability level without demanding additional computing cost for the reliability evaluation. The OSF equations are formulated considering RIA and PMA and extended to multiple failure case.Research Results. Several linear and nonlinear distribution laws are applied to composite yarns studies and then extended to multiple failure modes. It has been shown that the idea of the OSF method is to avoid the reliability constraint evaluation with a particular optimization process.Discussion and Conclusions. The simplified implementation framework of the OSF strategy consists of decoupling the optimization and the reliability analyses. It provides designers with efficient solutions that should be economic satisfying a required reliability level. It is demonstrated that the RBDO compared to OSF has several advantages: small number of optimization variables, good convergence stability, small computing time, satisfaction of the required reliability levels.

Reliability Evaluation of Regression Model for Estimating Co-seismic Landslide Displacement

Seismic coefficient values coupled with minimum pseudo-static safety factors are still used for analysis, where selection of seismic coefficients relies on expertise and judgment. However, safety factor approach does not give any idea about the deformations and displacements that are expected to occur during earthquake loading. Displacements are mostly evaluated by equations based on yield acceleration of the slope and maximum acceleration of sliding mass. In deterministic calculation, input information is considered as constant amounts as in cohesion, internal friction angle, slope and other characteristics. Due to the fact that co-seismic slopes deformation is a function of seismic yield coefficient ($$k_{\text{y}}$$) and other effective parameters, with the use of statistical analysis, the statistical distribution and standard deviation of $$k_{\text{y}}$$ can be calculated. In the current state of the art, in order to study the changes in slope reliability the following steps were taken: analyzing the pseudo-static of slope and other factors having different mechanical and physical parameters, determining the relationship between seismic yield coefficient of slopes and other parameters with the use of genetic algorithm and revolutionary algorithm, simulation of the factors effective on $$k_{\text{y}}$$ with specific statistical distribution applying Monte Carlo simulation using random number generator, determining statistic distribution and standard deviation of seismic yield coefficient of slope and finally determining the slopes failure probability based on allowable co-seismic slope displacement.

What’s the penalty for using the Square Root Law of inventory centralisation?

PurposeThe square root law (SRL) is a popular model for assessing inventory levels when changing the number of warehouses. Previous empirical research, however, has shown that mostly its underlying assumptions do not hold in practice. This sparks the question how inaccurate the SRL’s results are. The paper aims to discuss this issue.Design/methodology/approachIn 26 company cases of reducing the number of warehouses, the estimation error of the SRL is analysed irrespective of its underlying assumptions.FindingsThe analysis reveals an average estimation error for total inventory of 27.85 per cent (median=27.84 per cent), but a high variability across the cases. The SRL seems to mostly overestimate inventory savings from centralisation and inventory increases from decentralisation. Managers should only use the SRL if inventory depends on the number of warehouses in their situation, i.e. if they use the economic order or production quantity policy and safety factor approach. Suggestions for coping with the SRL’s estimation error are given.Research limitations/implicationsThis paper is based on the 26 cases that could be found in a thorough literature review in the ten most widely spoken languages and that contained or allowed to deduce the necessary information. In order to enable wider generalisations, this sample could be extended.Originality/valueMost past research has been more theoretical in nature. This research is the first to investigate the SRL’s estimation error using a variety of company cases and how to cope with this error.

A comparison of measured and predicted diffusion coefficients applied to sand and silt sized acid mine drainage materials

Determining the rate at which Acid Mine Drainage (AMD) sulfide oxidation occurs in mining waste products is a central requirement for safe and sustainable long term design of storages, including tails storage facilities, ore stockpiles and waste rock dumps. Inappropriate design can result in AMD acidification, mobilisation of heavy metals and pollution of ground and surface waters. The use of soil gas (oxygen) transport modelling to model AMD based sulfide oxidation and potential acidity loads is widespread, but diffusion coefficients used for modelling are based on existing diffusion coefficient models derived for natural and agricultural soils. Mining wastes are often well sorted due to mineral processing, and differences in soil structure and porosity can impact on diffusion coefficient behaviour compared to natural soils. This study compares a variety of approaches to estimate the diffusion coefficient and compare these results to measured values for comparison and analysis. A diffusion column apparatus is used to compare diffusion coefficient models from the literature with test results from the laboratory in several mining derived AMD materials. The results of the comparison indicate that laboratory testing of diffusion provides more accurate estimation of soil gas diffusion coefficients in mine materials. The use of diffusion coefficient safety factor approaches are explored as possible alternatives, if measurement of mine material matrix soil gas diffusion coefficient is not possible.

STABILITY CHARTS FOR UNSUPPORTED PLANE STRAIN TUNNEL HEADINGS IN HOMOGENEOUS UNDRAINED CLAY

ABSTRACT: This paper investigates the stability of plane strain tunnel headings in undrained soils. Using the factor of safety approach via the strength reduction technique, the idealised tunnel heading models are studied using the finite difference program FLAC. This problem is also similar to underground long wall excavations in plane strain condition. The finite difference results are presented alongside upper and lower bound limit solutions for validation. A thorough comparison between these two methods finds a very good agreement. Design charts are presented for a wide range of practical scenarios using dimensionless ratios, similar to Taylor’s design charts used for slope stability. Typical examples are presented to illustrate the usefulness for practising engineers.

A biomechanical model for maize root lodging

Root lodging is a structural failure of the root-soil anchorage system in a plant that adversely affects its yield. It is a complex phenomenon that depends strongly on both crop genetics and environmental factors. An accurate biomechanical model to predict root lodging would disentangle the component factors and improve development of lodging resistant plants, thereby reducing the constraint of root lodging on crop yields. We developed a biomechanical model that employs an engineering safety factor approach to quantify root lodging resistance as the ratio of anchorage supply and wind demand. We also conducted field experiments to parametrize the model for a sensitivity analysis and validate the model for predictive accuracy. The sensitivity analysis revealed primary, secondary, and tertiary factors for root lodging. The primary factors consisted of root angle, structural rooting depth, soil strength, and wind speed. The secondary factors were plant height, ear height, leaf area, stalk taper, ear mass, and leaf drag. Tertiary factors were stalk diameter and leaf number. The validation analysis found the model predictions compared well with data collected from three natural lodging events, with a goodness-of-fit of 0.58. The model effectively described a collection of natural lodging events, giving confidence in its predictive accuracy as well as the relative phenotypic and envirotypic influence factors determined in the sensitivity analysis. There are significant opportunities for model improvement, perhaps most significantly in the phenomenological understanding of the physical process.

Safety factor for structural elements subjected to impulsive blast loads

Design of blast loaded structures is usually carried out following a deterministic rather than a probabilistic approach. The design load scenario would cover the plausible load conditions (typically some conservative estimate) that a structure would experience if an explosion occurs but the probability that the structure will satisfy the design performances for the considered scenario remains unknown. Applying a performance-based design framework typically requires arduous Monte Carlo simulations, but a probabilistic design could also be achieved by a single structural analysis when consistent safety factors are applied to the load and the structural resistance. Such a factor is proposed herein for the case of components subjected to impulsive blast loads. The dependence of the safety factor on the amount of explosive, stand-off distance and their variability is estimated numerically and provided by means of regression formulas. A design example using the proposed safety factor is carried out and Monte Carlo simulation is used for verification. The results confirm the validity of the proposed safety factor approach and its applicability for the performance-based design of blast loaded structures using the current design practice methods.