Finite Element Limit Analysis Research Articles

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

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.

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 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.

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.]

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

A case study on soil slope landslide failure and parameter analysis of influencing factors for safety factor based on strength reduction method and orthogonal experimental design.

In civil engineering, stability analysis of slope is one of the main content of design. By using the finite element limit analysis software OptumG2, a landslide geological model is established to simulate the failure process of the landslide in Huadu District, Guangzhou City, China. The analysis focused on the deformation and failure characteristics, as well as the mechanical mechanism of landslide; the landslide mode of homogeneous soil is circular sliding. Additionally, investigating the influencing factors affecting slope stability is crucial in engineering implementation; in which the five influencing factors are considered as follow: slope height, slope gradient, soil cohesion, soil internal friction angle, and soil unit weight, respectively. A stability calculation model for a soil slope is established under 25 working conditions based on strength reduction method and orthogonal experimental design, in which the relationship between the safety factor and slope height, slope gradient, soil cohesion, soil internal friction angle, and soil unit weight is obtained. As the slope height increases from 5m to 45m, the safety factor of soil slope gradually decreases from 2.21 to 0.94; As the slope gradient increases from 20° to 60°, the safety factor of soil slope decreases approximately linearly from 1.80 to 0.95; As the cohesion of soil increases from 10kpa to 30kpa, the safety factor of soil slope increases approximately linearly from 1.04 to 1.60; As the internal friction angle of soil increases from 10° to 30°, the safety factor of soil slope increases approximately linearly from 1.00 to 1.81; As the unit weight of soil increases from 13kN/m3 to 21kN/m3, the safety factor of soil slope decreases approximately linearly from 1.50 to 1.21. The influencing factors affecting the safety factor of soil slope in descending order are slope height, slope angle, soil internal friction angle, soil cohesion, and soil unit weight. The research has reference significance for studying the stability and failure laws of soil slopes and conducting landslide control on soil slopes.

Coupling FELA and computation intelligent in predicting behaviour of inclination strip anchor in anisotropic and heterogeneous clays

This study introduces new numerical investigations of the uplift capacity of inclined strip anchors buried in anisotropic and heterogeneous clays. The analyses utilize Lower Bound (LB) Finite Element Limit Analysis techniques (FELA) under plane strain conditions, employing the Anisotropic Undrained Shear (AUS) failure criterion. The undrained shear strength of the clay increases proportionally with depth, and anisotropy is introduced by adjusting the ratios between the shear strengths obtained from three different tests. Four input parameters, namely, the embedment ratio (H/B), the inclination angle (α), the ratio of increasing undrained shear strength with depth (m = ρΒ/suTC0), and the factor of anisotropic parameters (re), are considered in analyzing the uplift coefficient (Fc), and a set of design charts is proposed. The effect of dimensionless parameters on the development of failure mechanisms is also investigated. Moreover, a novel method for assessing the ultimate uplift capacity of an inclined strip anchor in natural clay is given by integrating FELA with Multivariate Adaptive Regression Splines (MARS) and Extreme Gradient Boosting (XGBoost). Based on the optimal machine-learning models, this study also calculates the contribution of each input to the value of Fc via sensitivity analysis. The engineering computations for strip anchors embedded in anisotropic and non-homogenous clays can be improved with the results of these investigations and the proposed machine-learning models.

Novel neural network-based metaheuristic models for the stability prediction of rectangular trapdoors in anisotropic and non-homogeneous clay

The problem of trapdoor stability is a crucial problem in geotechnical engineering. This study is the first to introduce novel neural network-based metaheuristic models for the stability prediction of 3D rectangular trapdoors in anisotropic and nonhomogeneous clays. However, no researcher has considered such trapdoor problems in the past. In this study, the dataset is obtained by using finite element limit analysis (FELA). The proposed hybrid machine learning models based on artificial neural networks (ANNs) and various types of optimization algorithms (OAs), namely, ant colony optimization (ACO), artificial lion optimization (ALO), the imperialist competition algorithm (ICA), and shuffled complex evolution (SCE), are also proposed in this paper by undergoing rigorous optimization to ensure accuracy and efficiency in capturing the intricate dynamics of the stability investigations from the models. The performance of the proposed ANN-based models is assessed using several performance metrics, regression plots, and rank analysis. The proposed ANN-SCE model outperforms the other proposed models in predicting trapdoor stability, where the ANN-SCE model achieved the highest rank, with a score of 58, followed by the ANN-ALO (47), ANN-ICA (33), and ANN-ACO (22) models. The proposed neural network-based metaheuristic models deliver precise and effective forecasts of trapdoor stability to make informed decisions concerning road design and mitigation tactics, ultimately improving the robustness of infrastructure facing geotechnical challenges.

A modified Prandtl upper-bound solution of basal stability for narrow-deep excavations in undrained clay

In recent years, the construction of narrow-deep excavations has been steadily developing. Narrow-deep excavations exhibit a clear size effect in the basal heave stability analysis. However, the classical Prandtl mechanism ignores the size effect and influence of the inserted depth of wall penetration. Based on this, a modified Prandtl failure mechanism that considers the above factors was proposed in this study. Subsequently, a practical equation was derived to simplify the analysis process and obtain the safety factor against basal heave. The upper-bound solution provides a convenient and concise method for basal heave stability analysis of narrow excavations in undrained clay, and its feasibility was verified by comparing it with the results obtained by finite element limit analysis. The results showed that the proposed failure mechanism can provide a better upper-bound solution for the safety factor of the basal stability of narrow excavations than the classical Prandtl failure mechanism.

Developing a novel big dataset and a deep neural network to predict the bearing capacity of a ring footing

The accurate prediction of the bearing capacity of ring footings, which is crucial for civil engineering projects, has historically posed significant challenges. Previous research in this area has been constrained by considering only a limited number of parameters or utilizing relatively small datasets. To overcome these limitations, a comprehensive finite element limit analysis (FELA) was conducted to predict the bearing capacity of ring footings. The study considered a range of effective parameters, including clay undrained shear strength, heterogeneity factor of clay, soil friction angle of the sand layer, radius ratio of the ring footing, sand layer thickness, and the interface between the ring footing and the soil. An extensive dataset comprising 80,000 samples was assembled, exceeding the limitations of previous research. The availability of this dataset enabled more robust and statistically significant analyses and predictions of ring footing bearing capacity. In light of the time-intensive nature of gathering a substantial dataset, a customized deep neural network (DNN) was developed specifically to predict the bearing capacity of the dataset rapidly. Both computational and comparative results indicate that the proposed DNN (i.e. DNN-4) can accurately predict the bearing capacity of a soil with an R2 value greater than 0.99 and a mean squared error (MSE) below 0.009 in a fraction of 1 s, reflecting the effectiveness and efficiency of the proposed method.

Predicting uplift capacity of group anchors in sand using 3D FELA and MARS

Similar to pile group, the process of designing an anchor group requires the determination of an efficiency factor that describes the overlapping effects of neighboring anchors. This research article introduces an efficiency factor denoted as ξ, which represents the ratio of the ultimate uplift pressure of a single anchor within a group to the ultimate uplift pressure of an isolated anchor. The primary approach employed involves advanced 3D finite element limit analysis with an adaptive meshing technique, which can be utilized to examine the uplift stability problem of 3D anchor groups. Numerical findings are compared with those obtained from previous research, incorporating both experimental and analytical results. This would ensure that our results are validated and provide valuable information into the performance of anchor groups. In addition to these findings, we introduce a MARS machine learning model, which has been trained using a dataset of 875 data points. This model is designed to establish an empirical equation that can be practically used for design purposes. To further enhance our understanding, we present the relative importance index (RII). This index allows us to identify which factors have the most significant impact on the behavior of anchor groups. In conclusion, the results presented in this article are of practical significance for the geotechnical engineering community.

Probabilistic analysis of dual circular tunnels in rock masses considering rotated anisotropic random fields

Considering the spatial variability of rock masses in tunnelling analysis is a challenge in geotechnical engineering. This paper focuses on predicting collapse loads and probabilities of design failure for dual circular tunnels constructed in anisotropic rock masses. This study employs the random adaptive finite element limit analysis method, which incorporates rotated anisotropic random fields, to model uncertainties in rock mass properties. The generalised Hoek–Brown constitutive model is employed to define the yield failure criteria of a rock mass. The adaptive finite element limit analysis is first validated against a previous study, demonstrating good agreement. Then, the probability of design failure for dual circular tunnels is comprehensively investigated. This study emphasises the importance of considering both geometric parameters and rotated anisotropic random fields in comprehensive probabilistic analyses. The results provide insights into the mean and coefficient of variation of the stability numbers, as well as the probability of design failure for different geometric configurations and rotated anisotropic random fields. In conclusion, the variation in failure probability for practical applications is presented, highlighting the significance of accounting for spatial variability, rotation angle and anisotropy in rock mass properties in tunnelling.

Study on active earth pressure of narrow backfill of balance weight retaining wall under translational displacement mode

The balance weight retaining wall is a kind of gravity retaining wall. However, the theoretical results of the earth pressure are relatively few. The failure modes of backfill soil under different factors such as width to depth ratio of fill soil and rock inclination angle were studied by finite element limit analysis. Based on differential element methods and wedge limit equilibrium method, the active earth pressure calculation formula of balance weight retaining wall under translational displacement mode was derived. According to the parameter analysis, the interface friction resistance escalates alongside the rise in the boundary friction angle. The active earth pressure resultant force of the retaining wall increases with the increase of the width to depth ratio of filling, and decreases with the increase of the friction angle of filling. The design of counterweight retaining wall can benefit from the scientific basis and technical reference offered by the research findings.

Numerical analyses for three-dimensional face stability of circular tunnels in purely cohesive soils with linearly increasing strength

The tunnel face stability in purely cohesive soils with linearly increasing strength was investigated using three-dimensional finite element limit analysis (FELA). Both the collapse (active failure) and blow-out (passive failure) of the tunnel face were considered in the analysis. The rigorous upper bound (UB) and lower bound (LB) solutions of the load factor were calculated with a wide range of ground conditions to cover a broad scope of practical application. The results showed that the whole surface of the face is at failure in the collapse case; while in the blow-out case, there exists a gradual evolution process from partial failure to global failure within the tunnel face with increasing buried depth. Later, based on 960 finite element limit analysis results, a series of practical equations were proposed for tunnel face stability analysis in purely cohesive soils. These equations can be employed to quickly calculate the UB and LB solutions of the limit support pressure and the stability number of a tunnel face in both the collapse and blow-out cases. Finally, the calculation results from these equations were compared with those from previous studies in detail. The comparisons showed that the proposed equations make an improvement over existing methods and can be used as an efficient tool in practical engineering.

Stability Evaluation of Unlined Circular Tunnels in Sloping Rock Terrain Using Adaptive Finite Element Limit Analysis

Stability Evaluation of Unlined Circular Tunnels in Sloping Rock Terrain Using Adaptive Finite Element Limit Analysis

Stability analysis of slopes with cracks using the finite element limit analysis method

There are numerous slope projects involved in railway and highway constructions, and ensuring the stability of slopes, especially those with cracks, is very important. Compared with the limit equilibrium method, the limit analysis method takes into account the soil’s stress-strain behavior and boundary conditions, thereby yielding more rigorous and accurate results. The stability of slopes with cracks was examined using the finite element limit analysis method in this study. Results indicate that the stability of the slope decreases with the crack length, especially for slope with small slope ratio (i.e., α ≤ 1:1.5) and when lc/H exceeds 25%. The influence of crack inclination angle on slope stability increases with crack length, and the safety factor is larger in cases of negative inclination value cases as compared to those in positive inclination value cases when lc/H ≥ 0.33. Values of safety factor are larger in cases of slope with reinforcement as compared to those without reinforcement, and the values of F increase by about 20%. Additionally, the slip planes for slopes with reinforcement are located 10% further away from the slope surface compared to those without reinforcement, and reinforcements enhance the slope integrity.

Basal stability analysis of braced excavations with flexible embedded walls in undrained clay

An upper bound mechanism for the basal stability analysis in non-homogeneous undrained clay is presented. The current streamline-based velocity field formulas are extended into broader forms, allowing for the deformation compatibility between the wall and the soil. The proposed mechanism, comprising three shear zones, integrates consideration of the plastic bending moment of the embedded wall. The present study is validated by comparisons with solutions from the finite element limit analysis and elastoplastic finite element analysis. Results demonstrate that the proposed mechanism yields lower upper bounds compared to existing analytical methods, with predicted failure surfaces aligning well with elastoplastic finite element analysis and finite element limit analysis outcomes. Furthermore, a novel dimensionless number is proposed to quantify the relative strength of the plastic bending moment to soil undrained strength. Investigation into the influence of wall plastic bending moment, soil non-homogeneity, and wall penetration depth reveals beneficial effects. Following the analysis of case studies, it becomes evident that the proposed mechanism offers more dependable predictions compared to the existing circular upper bound mechanism.