Deterministic Stability Research Articles

Effect of weathering on the stability of rock slope at a water intake canal of Simplicio Hydroelectric Power Plant

Rock and joint alteration leads to modifications in their properties, resulting in a reduction of rock mass strength and consequently a decrease in the safety of engineering structures. The alteration process changes the material and alters its geomechanical behavior. This research presents the studies conducted to evaluate the mechanical behavior of rock joints in the gneiss massifs that make up the hydraulic circuit of the Simplicio Hydroelectric Plant due to their alteration. Compilation and analysis of data from previous research were carried out to parameterize the joints at different levels of alteration. Deterministic stability analyses showed that the alteration process of gneiss joints can significantly reduce the slope safety factor by up to half of its initial value. Furthermore, probabilistic analyses revealed an increase in failure probability of approximately 10% among the studied alteration classes. The results underscore the importance of assessing the level of joint alteration in engineering projects.

Stability analysis of uncertain simple pendulum equation *

The law of motion of a simple pendulum system is described by an uncertain simple pendulum equation which is a second-order uncertain differential equation driven by Liu process (LP). The stability of a simple pendulum system refers to whether the system tends to the equilibrium state under small perturbation. In order to discuss the sensitivity of the uncertain simple pendulum equation to the perturbation in the initial state, we give the concept of many kinds of stability of the uncertain simple pendulum equation, including almost deterministic stability, distributional stability and exponential stability. And, the sufficient conditions of almost deterministic stability, distributional stability and exponential stability of the uncertain simple pendulum equation are proved respectively.

Assessing the stability of the reservoir rim in moraine deposits for a mega RCC dam

<abstract> <p>Diamer Basha Dam is an under-construction, 272-meter-high, roller compacted concrete (RCC) dam on the Indus River in Pakistan. Once constructed, it will be the world's highest RCC gravity dam with a 105-kilometer-long reservoir. Most of the reservoir lies in unstable moraine deposits with steep slopes. Events like saturation during reservoir filling, alternate wetting, drawdown during reservoir operation, or a seismic event could trigger a large mass movement of these slopes into the reservoir to disrupt the dam functionality. This work identified the 15 most vulnerable slide areas using digital slope maps, elevation maps, and satellite imagery. Deterministic slope stability analysis was carried out on the identified sections under various stages of reservoir operation for static and seismic loading, using pseudo-static and dynamic analysis approaches. Probabilistic analysis was then performed using Monte Carlo simulation. The findings showed that most moraine deposits would collapse under reservoir filling, rapid drawdown, or seismic activity. Following the assessments, landslide susceptibility maps were generated, and an assessment of potential impacts, including the generation of dynamic waves, reservoir blockage, increased sediment loads, and reduced reservoir storage capacity, was also performed.</p> </abstract>

The impact of assumptions on deterministic and probabilistic analyses of earth fill embankments

This paper considers the impact of assumptions made when formulating analytic approaches to deterministic and probabilistic analyses of slope stability. The assumptions reviewed were presented in a paper, Waddell (2023) that presented semi-quantitative stability assessment using survey data, deterministic and probabilistic slope stability analyses of fill embankments constructed from residual soil and weathered bedrock in Western Sydney. A single variable fill strength was adopted, that was obtained from an Infinite Slope analysis assuming fully saturated fill. Rainfall records were used to predict risk of saturation to calculate annual probability of slope failure. The impacts of assumptions used to calculate the strength parameter, factor of safety and predicted failure probability are addressed in this paper. Saturation assumptions, the choice of limit equilibrium model, shape of the probability distribution functions, and spatial correlation of material properties are considered.

Universal abundance fluctuations across microbial communities, tropical forests, and urban populations.

The growth of complex populations, such as microbial communities, forests, and cities, occurs over vastly different spatial and temporal scales. Although research in different fields has developed detailed, system-specific models to understand each individual system, a unified analysis of different complex populations is lacking; such an analysis could deepen our understanding of each system and facilitate cross-pollination of tools and insights across fields. Here, we use a shared framework to analyze time-series data of the human gut microbiome, tropical forest, and urban employment. We demonstrate that a single, three-parameter model of stochastic population dynamics can reproduce the empirical distributions of population abundances and fluctuations in all three datasets. The three parameters characterizing a species measure its mean abundance, deterministic stability, and stochasticity. Our analysis reveals that, despite the vast differences in scale, all three systems occupy a similar region of parameter space when time is measured in generations. In other words, although the fluctuations observed in these systems may appear different, this difference is primarily due to the different physical timescales associated with each system. Further, we show that the distribution of temporal abundance fluctuations is described by just two parameters and derive a two-parameter functional form for abundance fluctuations to improve risk estimation and forecasting.

Probabilistic analysis of width‐limited 3D slope in spatially variable soils: UBLA enhanced with efficiency‐improved discretization of horn‐like failure mechanism

AbstractReliability analysis of earth slopes considering soil spatial variability has garnered significant attention from researchers. However, previous studies have predominantly focused on long slopes with infinite or ample width, such as dams and subgrades, but rare research was dedicated to slopes with width restricted by boundary constraints. In this regard, this paper proposes an efficient reliability framework suitable for width‐limited slopes in spatially variable soils. The proposed framework employed spatial discretization‐based upper bound limit analysis (UBLA) to conduct the deterministic slope stability analysis. The established failure mechanism can well capture the width‐limited three‐dimensional slip surface characteristics and satisfies the kinematically admissible conditions in spatially variable soils. Two innovative strategies are proposed to boost the efficiency of the discretized mechanism. They reduce the computational time to determine safety factors from over 20 min to less than 2 min. For the uncertainty modeling and slope reliability computing procedure, the Sparse Polynomial Chaos Expansion (SPCE) and Monte Carlo Simulation (MCS) methods are combined to generate the distribution of safety factors and failure probabilities. This combination addresses the high‐dimensional stochastic problem arising from 3D spatial variability. Using the proposed framework, a parametric analysis of a 3D spatially variable slope is conducted to investigate the impact of various factors. The findings of this paper are beneficial to the risk evolution of width‐limited slopes, and the efficiency enhancement strategies have the potential to expedite the limit analysis of other geo‐structures, such as tunnels, retaining walls, and foundations.

First order reliability-based design optimization of 3D pile-reinforced slopes with Pareto optimality

As verified structures for landslide mitigation, stabilizing piles are often adopted to treat local failure zones of width-limited soil slopes. To achieve a balance between slope safety and construction cost, an optimized piling scheme for treating width-limited soil slopes should be obtained through three-dimension (3D) stability analysis. In this regard, this paper presents a novel calculation framework for the multi-objective optimization (MOO) design of stabilizing piles. It is based on the first-order reliability method (FORM) and considers a 3D width-limited slope failure with geological uncertainties. The study first develops a deterministic 3D stability model of pile-reinforced slopes using limit analysis. Accounting for soil shear strength uncertainties, reliability analyses of 3D reinforced slopes are conducted based on the prescribed pile-reinforcement patterns. Then, a multi-objective probabilistic design procedure combining the Pareto front and reliability analysis results is proposed. The effectiveness and significance of the proposed MOO design framework are demonstrated through two illustrative examples: one involves designing stabilizing piles in a homogenous slope, and the other involves designing for an inhomogeneous earth slope with depth-dependent soil cohesion. To gain better understanding of the probabilistic impact of uncertain pile design parameters on reinforced slope stability, comprehensive parametric studies are conducted.

Hydrologic-geotechnical modelling of shallow landslide and flood hazards caused by heavy rainfall

Landslides and flooding are two of the most common hazards associated with heavy rainfall. Most studies, however, tackle the occurrence of these hazards separately or independently. Therefore, this study introduces a catchment-scale, multihazard approach that unifies the assessment of both phenomena through a combination of hydrological and geotechnical principles. By incorporating surface flow, infiltration, and slope stability analyses, the spatio-temporal response of both landslides and flooding during intense or heavy rainfall is characterized. To improve computational efficiency, a hybrid approach, consisting of the zero- and local-inertia flow models, is introduced to approximate the surface flow. Additionally, rainfall infiltration is estimated using the one-dimensional Green-Ampt model, and the results are incorporated in a deterministic slope stability analysis whose failure mechanism is generated from the forces arising from the effects of surface flow and the downward propagation of water along the assumed failure surface. The model is applied in the catchment of Marumori Town, Japan which suffered numerous landslide and flooding disasters during Typhoon Hagibis in 2019. The results indicate that the proposed model successfully simulates the hydrologic and geotechnical response of the catchment showing the distribution of both unstable slopes and inundated areas indicative of landslide and flooding hazards. The model’s capability to identify the timing and location of potential landslide and flood-prone areas could provide a practical framework for a unified early warning system, enhancing emergency planning and response efforts during heavy rainfall.

Exploring the performance of volatile mutations on evolutionary game dynamics in complex networks

The typical framework of replicator dynamics in evolutionary game theory assumes that all mutations are equally likely, meaning that the mutation of an evolving inhabitant only contributes constantly. However, in natural systems in biological and social sciences, mutations can arise due to their repetitive regeneration. The phenomenon of changing strategies (updating), typically prolonged sequences repeated many times, is defined as a volatile mutation that has been overlooked in evolutionary game theory. Implementing a repeated time framework introduces a dynamic mutation aspect incorporated with the pairwise Fermi rule. Network structure, ubiquitous in many natural and artificial systems, has significantly affected the dynamics and outcomes of evolutionary games. We examine the evolution of the pairwise game in terms of dilemma strength. It is revealed that mutation intensity can influence evolutionary dynamics. We also demonstrated that the obtained outcomes run by the deterministic and multi-agent simulation (MAS) process present similar stability regions for both linear and non-linear dynamics, even in various game classes. In particular, the most stimulating effect is detected for the relationship between the fraction of cooperation and the fraction of the mutated individuals, as inclination tends to provide an increasing tendency and supporting defection in the opposite case. In conclusion, we identified a form of volatile mutation as a form of noise that, under certain situations, could be used to enhance cooperation in social systems and design strategies for promoting cooperation in networked environments.

Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems

This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT systems is certified. Extensions to systems under deterministic perturbations as well as stochastic noise are then considered. For the former, sensitivity to perturbations for fixed-time stable DT systems is analyzed, and it is shown that fixed-time attractiveness results from the presented Lyapunov conditions. For the latter, sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented. The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixed-time attractive systems, and a stochastic settling-time function fixed upper bound is derived for stochastic DT systems. Illustrative examples are given along with simulation results to verify the introduced results.

Back-analysis of a rainfall-induced landslide case history using deterministic and random limit equilibrium methods

Because recurrent rainfall-induced landslide episodes mimic prior failures, this study builds a back-analysis approach to identify those prior failure events and assess the prospective slope performance going forward. Engineers use the results of this approach to project the slope performance based on the quantity of rainfall accumulation during the anticipated rainfall event. A landslide case that occurred in 2004, as a result of a typhoon event, was selected for the back-analysis procedure. Four typhon events were chosen to simulate the pore water pressure conditions, which may have caused damage of varying severity (including landslide failure) to the slope. The numerical model was initially analyzed via the deterministic limit equilibrium slope stability approach to evaluate the most critical failure surface. By adopting the Monte Carlo simulation approach, the following step assessed the random limit equilibrium slope stability on the most critical failure surfaces. The probabilistic distributions of the safety factor were then generated for each typhoon event. Subsequently, the simulation outcomes provide safety indicator values incorporating the mean safety factor, failure probability, and reliability index. From the failure probability and reliability index, a zonation approach with various site-specific performance levels were established by using the corresponding accumulated rainfall to define the exceedance threshold values for each zone. In order to confirm the site-specific performance, we compared the normalized error values acquired from the analysis technique to those measured under two recent typhoon occurrences. An acceptable consistency was attained, validating the procedure's appropriateness for future rainfall events.

Bulkheads’ Position Optimisation in the Concept Design of Ships under Deterministic Rules

The position of the transverse bulkheads is the most important aspect in determining the internal subdivision of the ship and has a strong impact on the general arrangement, weight distribution and capacity of the ship. Nowadays, deterministic rules still apply to various types of ships such as gas carriers, naval ships, icebreakers, etc. For these vessels a new floodable length can be defined as the extent of the ship that can be flooded, still assuring compliance with the damage stability criteria. The main objective of this paper is using the floodable lengths to optimize the position of bulkheads. The proposed methodology maximises the margin between the floodable length and the actual flooded length, which consists of two lost contiguous compartments. This method, applicable in the framework of multi-attribute decision-making techniques for ship concept design, allows identification of the minimum number of bulkheads a ship requires, quantification, and maximisation of the safety margin for compliance with deterministic damage stability criteria. This margin ensures maximum flexibility for changes that may be required in the next design phases. The proposed method, based on a multi-stage optimization, is tested on a compressed natural gas carrier to define the minimum number and position of the transverse bulkheads dividing the cargo holds.

Deterministic and stochastic analysis of a modified Leslie–Gower predator–prey model with Holling‐type II functional response

This paper aims to study the deterministic and stochastic features of a modified Leslie–Gower predator–prey model with Holling‐type II functional response. We first investigate the dynamical properties of the deterministic model, including existence and stability of the equilibrium, and different types of bifurcations. For the stochastic model, a phenomenon of noise‐induced state transition is found. By applying the stochastic sensitivity functions technique, we construct the confidence domain of stochastic attractor and then estimate the critical value of the intensity of noise generating this transition. Numerical simulations are performed to validate the analytical findings.

Chewing Khat Transmission Dynamics: A Mathematical Model and Stability Analysis

In this study, the authors proposed a nonlinear deterministic model and stability analysis for the transmission dynamics of chewing khat. The model’s solution is proved to be positive and bounded, and the basic reproduction number ( R 0 ) is calculated using the next-generation matrix method. Following that, the authors have looked at the local and global stability of the model’s khat-free and endemic equilibrium points. When R 0 < 1 , the chewing khat-free equilibrium point is locally and globally asymptotically stable, whereas when R 0 > 1 , the endemic equilibrium point is locally and globally asymptotically stable. The simulation results demonstrate the analytical results.

Application of interval field method to the stability analysis of slopes in presence of uncertainties

Spatial uncertainty of soil parameters has a significant impact on the analysis of slope stability. Interval field analysis is emerging as a complementary tool of the conventional random field method that can take spatial uncertainty into account, which, however, has not been investigated in slope stability analysis. The present paper proposes a new method, named the interval field limit equilibrium method (IFLEM), for assessing the stability of slope in the presence of the interval field. In this method, the modified exponential function is introduced to characterize the spatial uncertainty of the interval field and the Karhunen–Loève-like decomposition is employed to generate the interval field. Then, in a single calculation, the deterministic slope stability analyzed by the Morgenstern–Price approach is implemented in order to estimate the safety factor. Subsequently, the upper and lower bounds of the interval of safety factor are efficiently evaluated by a kind of surrogate-assisted global optimization algorithms, such as Bayesian global optimization used in this study. Finally, the effectiveness of the proposed method is verified by three numerical examples. The results indicate that the proposed method can provide reasonable accuracy and efficiency, which is potentially applicable to a number of geotechnical systems.

Deterministic and probabilistic basal heave stability analysis of circular shafts against hydraulic uplift

Circular shafts are commonly required for urban development. Their construction often encounters underground water, which can make shafts more prone to hydraulic heave and to soil uplifts which may cause serious accidents. Therefore, the basal heave stability analysis of shafts subjected to a hydraulic uplift is essential to ensure their safety. In this study, deterministic and probabilistic analyses of supported circular shafts in clayey soils subjected to hydraulic uplifts are presented. The effects of the permeability anisotropy coefficient (rk), the soil-wall interface strength coefficient (ri) and the soil tension cut-off coefficient (rt) are discussed. The basal heave safety factor is evaluated by a Finite Element Limit Analysis (FELA). A Stochastic Finite Element Limit Analysis (SFELA) is introduced to perform the probabilistic analyses by coupling the FELA, an adaptive Polynomial Chaos Kriging (PCK), the Monte-Carlo Simulations (MCS), the First Order Reliability Method (FORM) and the Global Sensitivity Analysis (GSA). It is then carried out to get valuable probabilistic results. Several academic cases are considered: (1) effects of rk on the flow vectors, seepage pressures and water head distributions; (2) effects of rk, ri and rt on the shaft stability considering by safety factor and failure probability; (3) importance rank of rk, ri, soil cohesion and friction angle. The results indicate that the permeability anisotropy coefficient, the soil-wall interface strength and the tension cut-off have a remarkable influence on the circular shaft stability when a hydraulic uplift is considered.

Efficient reliability‐based design of slope angles in spatially variable soils with field data

AbstractDeterministic single factor of safety method cannot explicitly account for the influences of various sources of uncertainties (e.g., spatial variability of geomaterials, measurement and transformation uncertainties) in stability design of slopes. Many probabilistic methods have been applied to the reliability‐based design (RBD) of slopes, but they typically require performing numerous deterministic slope stability analyses. In this paper, an efficient reliability‐based design method for spatially varying slopes based on field data is proposed. Here, the RBD of a slope angle is concerned. Reliability‐based design is implemented using an inverse First Order Reliability Method (inverse FORM ‐ IFORM). A sandy slope and a cohesive slope are investigated as examples, respectively, to illustrate the proposed method. The results indicate that the proposed method can quickly obtain rational design schemes of slope angles accounting for the spatial variability of soil properties, measurement and transformation uncertainties based on the field data. It can act as a practical and effective tool for the RBD of slopes in two‐dimensional spatially variable soils. Additionally, it is found that the random field mesh size affects the RBD results significantly, while the probability distribution and horizontal autocorrelation of soil parameters have slight influences on the RBD results.

Personality Models in the Context of Child and Adolescent Psychiatry - Development, Change, Stability and Research Perspectives

Personality models play an important role for the etiological understanding of abnormal development in clinical settings. In this selective review, relevant personality models are presented and, in particular, their developmental dynamics and adaptability over the life span, starting in childhood, are considered in detail. The focus is on the developmental psychopathological perspective of processes of ego-resiliency and self-regulation between the poles of disposition and social environment. This is particularly obvious in the discussion of developmental path models of personality dysfunction with experiences of abuse or disorganized attachment in the child's history. Psychopathologically, an ongoing impairment of self-regulation often results in stable patterns of maladaptation, which leads in the case of purely symptomatic treatment usually only to temporary behavioral modifications. On the other hand, the changeability of pathological personality traits through the use of targeted intervention approaches will favour of a positive outcome and contradicts a deterministic stability of personality characteristics. For future research perspectives in developmental psychopathology, various theoretical personality constructs are discussed and linked to clinical observations.

Evaluating Rock Mass Properties of Vipingo Coral Limestone Quarry Based on a Modified Geological Strength Index (GSI) and State of Karstification

The process of evaluating rock mass strength requires that major structural features such as joints that influence rock strength are considered. In carbonate rock masses, however, the strength of the rock mass is largely dependent on intact rock strength and structural features play a secondary role. Laboratory experiments on porous rock have shown that intact rock strength reduces with increasing porosity, which has a direct effect on the rock mass strength. Rock porosity has however not been well accounted for in rock mass characterization methods currently in use. This research applies the modified GSI method for carbonate rock masses which is based on a combination of GSI and total porosity. The main aim is to quantify the GSI with respect to rock porosity which is a direct indicator of the state of karstification, as an inherent feature that affects rock mass strength. An empirical equation is proposed whereby the GSI as observed in the field is modified by a natural log of the value of porosity, giving rise to a modified GSI (GSIm). The GSIm together with laboratory properties of rock is used to determine the properties of Vipingo coral limestone from RocLab software. A deterministic parametric slope stability analysis is done using the finite element software Phase 2 with the rock mass properties as input parameters. The analysis results point to a direct dependence of the slope stability on slope angle, slope height and rock mass strength of the lithological unit. The graphs make a useful design guide for slopes engineered in this type of rock mass.

Assessment of maintenance efforts and probabilities of failure at German inland waterways to advance the design of bank revetments

Revetments protect waterways or flood defenses against erosion from waves and currents. In Germany a high percentage of about 7235 km of waterways is secured by revetments. Like many stakeholders of various infrastructures, the German Federal Waterways and Shipping Administration increasingly aims for a more economic and ecological design and maintenance strategy. Thus, new methodologies must be introduced that relate the structural condition of the revetment to resulting consequences such as required maintenance. In this paper we investigate the correlation of maintenance and revetment stability. Using the example of German inland waterways, maintenance measures conducted over at least six years are correlated with a deterministic and a probabilistic stability assessment. To account for realistic traffic loads, the stability assessment employs field measurements which provide data on ship-induced waves. It was found that at least a linear correlation between revetment stability and maintenance must be assumed. A comparison between the deterministic and the probabilistic stability assessment and thereby obtained correlations shows that less maintenance is predicted with the deterministic stability assessment. Particularly for small sample sizes and small probabilities of failure, the probabilistic approach should be favored over the deterministic approach to account for various uncertainties. In the case that only maintenance is of relevance for design considerations, the results of the probabilistic approach indicate that β = 1.3 (pf ≈ 10-1) may be a suitable annual target reliability.