Finite Element Limit Analysis Research Articles

A two-step dynamic FEM-FELA approach for seismic slope stability assessment

AbstractThe determination of the factor of safety (FoS) of slopes during seismic excitation can be complex if the relevant effects of pore water pressure accumulation, nonlinear material response and variable shear strength are duly accounted for. A rational two-step approach to tackle this task based on a hydro-mechanically coupled dynamic simulation and finite element limit analyses is henceforth introduced. To ensure accurate transfer of the hydro-mechanical soil state, a mapping concept is presented, accounting for spatial distributions of stresses, excess pore water pressures, inertial forces and shear strength. The proposed approach is compared to limit equilibrium method (LEM) for the case of a large-scale water-saturated open cast mine slope subjected to seismic loading. In comparison with LEM, the new approach to assess seismic slope stability proves to be simpler in its implementation and straightforward, which could be an important asset for practitioners.

Effects of inclined loads on strip footings with an underlying tunnel

The self-developed Finite Element Limit Analysis (FELA) code was utilized to examine the ultimate bearing capacity of strip footings positioned above tunnels affected by inclined loads. Bearing capacity factors were predicted using both upper bound (UB) and lower bound (LB) solutions, with a variance of less than 3 %. The primary focus of this study lies in assessing the influences of underlying tunnels and inclined loads on potential failure modes. In particular, the concept of failure envelopes was introduced, by which the load properties (inclination angle), the tunnel location (relative lateral distance and longitudinal distance from the footing) and the material properties of rock masses (GSI, mi, sci, g) were involved in to facilitate preliminary designs. In addition to envelopes, the transition among failure patterns was summarized, resting with any possible factors.

Development of an improved limit pressure solution for shape-distorted 90o pipe bends with through-wall circumferential cracks

PurposeThis paper presents the approximate limit pressure solution for shape-imperfect and through-wall circumferential cracked (TWCC) 90° pipe bends at the intrados region. Finite element (FE) limit analysis was used to estimate the limit pressure by considering the small geometrical change effects.Design/methodology/approachThree-dimensional (3D) geometric linear FE methodology was implemented to investigate the limit pressure of structurally deformed TWCC 90° pipe bends. The material considered in the analysis is elastic perfectly plastic (EPP). The limit pressure of TWCC shape-distorted pipe bends was predicted from the corresponding internal pressure when von-Mises stress was equal to or just exceeded the material’s yield strength for all the models. The theoretical solution which was published in the literature was used to evaluate the current FE approach.FindingsOvality Co and TWCC at the intrados region caused a considerable impact on pipe bends, while the thinning? Ct produced a negligible effect and hence was not included in the analysis. With the combined effect, the bend portion of pipe bend experiences substantial influence, and the TWCC effect consequently increases with 45o, 60o and 90o crack angles and decreases the limit pressure of pipe bends. An improved closed-form empirical limit pressure solution was proposed for TWCC shape-distorted pipe bends at the intrados region.Originality/valueIn the limit pressure analysis of 90° pipe bends, the implications of structural irregularities (ovality and thinning) and TWCC have not been examined and reported.

Stability analysis of tunnel heading in clay with nonstationary random fields of undrained shear strength

The stability problem of a tunnel heading in clay remains a significant challenge in geotechnical engineering. Specifically, when considering the spatial variability of the soil, the stability factor may be influenced by geographically random fields. This study investigates the effect of random fields on a probabilistic analysis of a tunnel heading in undrained clay. The study assumes that the undrained shear strength of the clay increases linearly with depth due to a strength gradient factor. The random adaptive finite element limit analysis is employed to calculate the stability numbers for tunnel headings. Nonstationary random fields with varying vertical correlation lengths are simulated using Monte Carlo simulation technique. The stability analysis takes into account geometry parameters (i.e., cover depth ratio) and nonstationary random field of undrained shear strength parameters. (i.e., strength gradient, coefficient of variation, and vertical correlation length). The results of tunnel face stability using random adaptive finite element limit analysis have also been utilised to assess the probability of design failure over a practical range of deterministic factors of safety. In the context of probabilistic failure analysis, the failure mechanism resulting from varying vertical correlation lengths could influence the probability of design failure. The findings of this study can be of significant interest to tunnel engineering practitioners during the design phase of tunnel heading projects.

Hybrid artificial neural network models for bearing capacity evaluation of a strip footing on sand based on Bolton failure criterion

This paper employs the Bolton failure criterion, incorporating strength-dilatancy relationships, to analyze the bearing capacity factor of a strip footing on dense sand. Utilizing finite element limit analysis (FELA) based on the lower and upper bound theorems, the study presents the results as average bound solutions. By using the Bolton model, the b parameter is first calibrated and found that it should be about 3.50 to align the ultimate bearing capacity (qu) from FELA to have a good agreement with that from experimental test results from previous studies. The influence of parameters relevant to the Bolton failure criterion is analysed, showing that an increase in relative density (DR) significantly affects the variation in the bearing capacity factor (Nγ) at higher Q values, while lower Q values inhibit dilatancy due to soil crushing. The width of the strip footing (B) has a decreasing effect on Nγ at higher Q values, and the unit weight (γ) changes minimally impact Nγ within the range of 16–22 kN/m3. Additionally, an increase in the critical state friction angle (ϕcv) consistently increases Nγ, highlighting its direct correlation with soil shear strength. A hybrid artificial neural network (ANN) model integrates machine learning with four optimization algorithms: Imperialist Competitive Algorithm (ICA), Ant Lion Optimization (ALO), Teaching Learning Based Optimization (TLBO), and New Self-Organizing Hierarchical Particle Swarm Optimizer with Jumping Time-Varying Acceleration Coefficients (NHPSO-JTVAC). Comparative rank analysis of hybrid ANN models based on the selection of the optimal number of hidden neurons demonstrates that the ANN-TLBO model excels in predicting the bearing capacity factor, achieving a score of 48. This conclusion is corroborated by an error heatmap matrix, which indicates a minimized percentage of error relative to other hybrid ANN models. Importance analysis identifies particle crushing strength (Q) as the most significant factor influencing the bearing capacity factor (Nγ).

Probabilistic ultimate lateral capacity of two-pile groups in spatially random clay

ABSTRACT The undrained lateral capacity of a group of two side-by-side piles has been studied in uniform clay, but the effect of spatial variability in clay strength on lateral pile capacity remains unclear. This paper describes probabilistic ultimate lateral capacity for two circular piles in spatially variable undrained clay. An adaptive finite element limit analysis based on random field generation combined with Monte Carlo simulations is applied. The lateral capacity statistics of two-pile groups with different combinations of pile spacings and pile roughness are presented. It is found that the consideration of the random nature of clay strength leads to a significant decrease in the lateral pile capacity, especially at a pile spacing approximately equal to the pile diameter. The factor of safety required to attain a target probability of failure is provided as a function of pile spacing. The obtained results give guidance for the reliability-based design of laterally-loaded two-pile groups in spatially varied clay and can also be applicable for understanding the lateral translation of two interfering cables and pipelines deeply buried in random clay.

Novel hybrid XGBoost-based soft computing models for predicting penetration resistance of buried pipelines in cohesive soils

In this paper, both the finite element limit analysis (FELA) and soft computing techniques of four hybrid XGBoost (XGB) models, namely, GA-XGB, optimized with Genetic Algorithms; SMA-XGB, optimized with Slime Mould Algorithms; PSO-XGB, optimized with Particle Swarm Optimization; ACO-XGB, Ant Colony Optimization; and one Genetic Programing model (GP), are employed to develop surrogate models for predicting the undrained penetration resistance of buried pipelines embedded in clays. The penetration resistance of pipelines is caused by internal and external pressures, resulting in a force that acts on the pipeline in the downward and inclined directions at the same time. The penetration resistance factor (N) of a buried pipeline is determined based on four dimensionless variables, namely, the buried depth ratio (H/D), the inclination angle of the applied load (β), the soil strength or overburden ratio (γH/c), and the adhesion factor at soil-pipeline interfaces (α). The findings of this study are presented and summarized in the form of charts for dimensionless penetration resistance factors (N) and failure mechanisms of pipelines. Furthermore, the results from this study are compared with the results from previous studies and agrees well with those of previous studies. According to the results of the four developed hybrid XGBoost-based models, SMA-XGB outperforms GA-XGB, PSO-XGB, and ACO-XGB with no symptoms of overfitting, while the GP model resulted in an adequately accurate model with the advantage of a closed-form equation; its determination correlation coefficient of training and testing equals 0.98 (R2 = 0.980).

FELA evaluated bearing capacity factors for circular, planar, and interfering cutting edges of open caisson

ABSTRACT In the study, a thorough analysis of the drained bearing capacity factors of cutting edges of open caissons with and without interference has been carried out which helps in planning the controlled sinking of caissons. Five different conditions are analysed in this study: single circular, single planar, V-shape planar, interfering planar, and interfering V-shape planar cutting edges. Implementing upper and lower bound finite element limit analysis (FELA) in accordance with Terzaghi's conventional bearing capacity equation, the bearing capacity factors of the cutting edge of open caissons are evaluated. The design charts for the bearing capacity of cutting edges are determined by accounting for the effects of the radii ratio of the circular caisson, distance ratio of planar cutting edges, cutting angle of cutting edge, soil internal friction angle, and spacing between the cutting edges. The soil failure planes corresponding to the aforementioned aspects of the cutting edges are also evaluated.

Investigation on the failure mechanism for surrounding rock in small interval tunnels using finite element limit analysis method

This paper presents a case study to evaluate the failure mechanism of surrounding rock in mountain tunnels caused by small interval parallelism and the reinforcement effect of intermediate rock columns. The characteristics and reasons of surrounding rock collapse were analyzed through field investigation, taking Yaoxi Tunnel as a case study. The critical collapse and blowout pressure results obtained by the finite element difference method (FEDM) software FLAC and the finite element limit analysis method (FELAM) software OPTUM were compared based on Mollon’s theoretical solution. The critical support pressure errors for collapse are 18.803% and 8.129%, indicating that OPTUM has a slight advantage in accuracy for solving tunnel collapse. Therefore, the models of small interval tunnels were established by OPTUM to investigate the collapse failure mechanism and progressive failure process of surrounding rock. The effects of tunnel depth ratio (H/D), spacing ratio (S/D), and surrounding rock parameters (γ, φ, c) on critical support pressure, failure mode, and surrounding rock settlement laws were studied through simulation models. It shows that the gradual decrease in mechanical parameters of rock is the main cause of the increase in critical support pressure. The design parameters (H/D, S/D) have a mutagenic effect on the pressure arch of the double tunnel surrounding rock. As the distance between the two holes increases, the joint pressure point in the intermediate rock column gradually rises. Finally, the effectiveness of the reinforcement measures for the intermediate rock column was verified through on-site monitoring. The research results of this study have reference price for similar projects.

Failure envelopes of rigid tripod pile foundation under combined vertical-horizontal-moment loadings in clay

The problem considered in this computational study is for the bearing capacity determination of three-dimensional (3D) rigid tripod-pile groups subjected to combined vertical (V), horizontal (H), and bending moment (M) loads. Using the adaptive 3D finite element limit analysis (FELA) coupled with lower bound, upper bound and mixed Gauss element formulations, numerical results are compared with those of the previous study under a single-component loading (V, or H, or M). The failure envelope in the 3D V–H–M loading space is then constructed, and several failure mechanisms presented to complement the discussions on the complex 3D responses. This is followed by a parametric study for the various factors such as the pile length, pile spacing, pile-soil adhesion factors as well as the loading direction angle. Finally, a closed-form design expression of failure envelopes considering the abovementioned influential parameters and the combined load are derived. Noting that the current industry-based design procedures for tripod-pile groups are rarely found, the outcome of the present study can be used with great confidence in design practice.

Evaluating the impact of eccentric loading on strip footing above horseshoe tunnels in rock mass using adaptive finite element limit analysis and machine learning

Evaluating the impact of eccentric loading on strip footing above horseshoe tunnels in rock mass using adaptive finite element limit analysis and machine learning

Study on the differences between Hoek–Brown parameters and equivalent Mohr–Coulomb parameters in the calculation slope critical acceleration and permanent displacement

Mohr–Coulomb (MC) strength criterion has been widely used in many classical analytical expressions and numerical modeling due to its simple physical calculation, but the MC criterion is not suitable for describing the failure envelope of rock masses. In order to directly apply MC parameters to analytical expressions or numerical modeling in rock slope stability analysis, scholars established a criterion for converting Hoek–Brown (HB) parameters to equivalent MC parameters. However, the consistency of HB parameters and equivalent MC parameters in calculating critical acceleration of slope needs to be further explored and confirmed. Therefore, HB parameters are converted into equivalent MC parameters by considering the influence of slope angle (1# case and 2# case when slope angle is not considered and slope angle is considered respectively). Then, the lower-bound of finite element limit analysis is used for numerical modeling, and the results of calculating critical acceleration using HB parameters and equivalent MC parameters are compared, and the influence of related parameters on the calculation of critical acceleration is studied. Finally, the influence of different critical accelerations on the calculation of slope permanent displacement is further analyzed through numerical cases and engineering examples. The results show that: (1) In the 1# case, the critical acceleration obtained by the equivalent MC parameters are significantly larger than that obtained by the 2 #case and the HB parameters, and this difference becomes more obvious with the increase of slope angle. The critical acceleration obtained by the 2# case is very close to the HB parameters; (2) In the 1# case, slope height is inversely proportional to ΔAc (HB(Ac) − 1#(Ac)), and with the increase of slope height, ΔAc decreases, while in the 2# case, the difference of ΔAc (HB(Ac) − 2#(Ac)) is not significant; (3) In the 1# case, the sensitivity of the HB parameters to ΔAc is D > GSI > mi > σci, but in the 2# case, there is no sensitivity-related regularity; (4) The application of HB parameters and equivalent MC parameters in slope permanent displacement is studied through numerical cases and engineering examples, and the limitations of equivalent MC parameters in rock slope stability evaluation are revealed.

Innovative approaches for predicting seismic stability of circular and rectangular tunnels in cohesive-frictional soils using machine learning and finite element limit analysis

Innovative approaches for predicting seismic stability of circular and rectangular tunnels in cohesive-frictional soils using machine learning and finite element limit analysis

Probabilistic assessment of bearing capacity of skirted foundation under combined loadings with a rigid base

Skirted foundations are critical components in offshore applications where combined loads are common in deep‐water environments. Their ultimate capacity under VH (vertical‐horizontal) combined loading is traditionally determined using VH failure envelopes, which are primarily constructed using numerical methods. These methodologies, however, frequently ignore the spatial variability inherent in seabed soils due to geological formations. This paper investigates the effect of spatial variability of undrained shear strength and embedment ratio impact on the capacity of skirted foundations subjected to VH combined loading. For this, OptumG2 software is used to perform Monte Carlo simulation combined with random finite element limit analysis. This paper investigates the stochastic analysis of bearing capacity and failure envelopes, with a particular emphasis on understanding the effect of spatial correlation on undrained shear strength. The study focuses on the horizontal scale of fluctuation and the soil strength heterogeneity index, shedding insight on previously undiscovered areas. Novel findings highlight how a rigid base affects VH failure envelopes and offer insights into evaluating the vertical bearing capacity of skirted foundations. [Correction added on 8 July 2024, after first online publication: The above statement has been updated in this version.]

Data-driven modelling of bearing capacity of footings on spatially random anisotropic clays using ANN and Monte Carlo simulations

ABSTRACT The fundamental issue of bearing capacity of footings on anisotropic clays holds significant importance in geotechnical engineering. Previous investigations predominantly focused on deterministic analyses, disregarding the spatial variability of soil. A probabilistic analysis of the bearing capacity of footings is conducted in this paper, incorporating the spatial variability of anisotropic clays. To achieve this, Random Adaptive Finite Element Limit Analysis (RAFELA) and Monte Carlo simulations are utilised to capture the full spectrum of potential outcomes under parametric uncertainty. The impact of anisotropic soil strength variability is explored across three input parameters such as the anisotropic strength ratios, coefficients of variation, and dimensionless correlation lengths. In order to establish surrogate models capable of predicting random bearing capacity of anisotropic clays, Artificial Neural Network (ANN) models are developed. The use of the proposed ANN surrogate models presents a more convenient and computationally efficient approach for predicting the ultimate vertical load of footings on spatially random anisotropic clays.

Material optimization of reinforced concrete structures in multiple limit states

AbstractA common limitation in current material optimization methods for reinforced concrete structures is that they often concentrate solely on either the serviceability limit state (SLS) or the ultimate limit state (ULS). In response, this paper introduces a novel approach to optimize the material layout in planar reinforced concrete structures in plane stress, accounting for both limit states simultaneously. The proposed method employs an iterative strategy, integrating criteria for serviceability and ultimate limit states while approximating the elastoplastic behavior of cracked reinforced concrete. Here, the criteria for the limit states are incorporated as limits on the strains. The methodology initiates with a finite element limit analysis for the preliminary layout. The minimum potential energy principle is utilized to determine the strains for the nonlinear material response, and subsequently, an iterative linearized method is applied for material optimization. The research showcases the successful application of this approach to simple examples and presents improved and optimized solutions that adhere to the limit criteria for more complex structural scenarios.

Evaluation of seismic bearing capacity of strip footing on soil slope using finite element limit analysis

Evaluation of seismic bearing capacity of strip footing on soil slope using finite element limit analysis

STABILITY ASSESSMENT OF ROOT-REINFORCED SLOPES USING FINITE ELEMENT LIMIT ANALYSIS

Slope instability poses serious threats to infrastructure and environmental sustainability. As a result, numerous reinforcement techniques have been used as disaster mitigation attempts to prevent slope failure. Among various traditional slope reinforcement methods, the use of vegetion root is more cost-effective and environmentally friendly. This paper presents stability assessment of root-reinforced slopes. Firstly, slope models were built for case of bare and root-reinforced slopes. The slope angles were varied in the range of 15º ~ 55 º. The root cohesion and depth of root zone were adjusted within the ranges of 0 ~ 20 kPa and 0 ~1.5 m, respectively. The strength reduction finite element limit analysis method was applied to evaluate the stability of the slopes in this study. The results indicate that factor of safety increases with the increasing of root cohesion and depth of root zone. The best factor of safety was obtained for the case with root cohesion and depth of root zone of 20 kPa and 1.5 m, respectively. Shear dissipation contours of the slope models also show that root reinforcement reduces shear dissipation energy along the failure surface, consequently lowering the possibility of slope failure.

Active failure mechanisms and earth pressure of narrow backfill behind retaining structures

Through a series of model tests accomplished by particle image velocimetry analyses, this study presents the visualisation of the displacement field of narrow soil behind retaining structures under translational mode. The progressive development of failure mechanisms and active earth pressure are measured in the process of tests. Finite-element limit analyses are additionally carried out to investigate and verify the ultimate failure mechanism and active earth pressure acting on retaining structures. Furthermore, this study carried out analyses on the development of failure mechanisms and active earth pressure with different aspect ratios, inclinations of the existing structure and backfill surface surcharge. A reasonable agreement was observed between experimental and numerical results. With an increase in backfill spacing, the failure mechanism of backfill turns from reflective shear bands into a single shear band, and the earth pressure exerted on the retaining structure increases.

Upper Bound Finite Element Limit Analysis of the Response of Shallow Foundations Subjected to Dip-Slip Reverse Fault Rupture Outcrop

Upper Bound Finite Element Limit Analysis of the Response of Shallow Foundations Subjected to Dip-Slip Reverse Fault Rupture Outcrop