Adaptive Finite Element Limit Analysis Research Articles

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.

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.

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

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.

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.

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

Undrained stability of braced excavations in clay considering the nonstationary random field of undrained shear strength

The basal heave stability of supported excavations is an essential problem in geotechnical engineering. This paper considers the probabilistic analysis of basal heave stability of supported excavations with spatially random soils by employing the random adaptive finite element limit analysis and Monte Carlo simulations to simulate all possible outcomes under parametric uncertainty. The effect of soil strength variability is investigated for various parameters, including the width and depth of the excavation ratio, strength gradient factor, and vertical correlation length. Probabilistic basal stability results have also been employed to determine the probability of design failure for a practical range of deterministic factors of safety. Considering probabilistic failure analysis, the more complete failure patterns caused by the various vertical correlation length would decrease the probability of design failure. There are different tendencies between the probability of design failure at the same safety factor with various vertical correlation lengths. These results can be of great interest to engineering practitioners in the design process of excavation problems.

Seismic bearing capacity for strip footings above voids in cohesive-frictional soils

In this article, the seismic bearing capacity for strip footings above square voids in cohesive-frictional soils is presented. A numerical study is performed by using adaptive finite element limit analysis (AFELA), and the pseudostatic approach is employed to consider the earthquake loadings. Both the upper bound (UB) and lower bound (LB) of the seismic bearing capacity for the strip footing are obtained, along with the relative errors, which are found within 8% or less. The results are presented in the form of design tables and charts to be used by designers and practicing engineers. The effects of the location of the voids, the dimensionless strength ratio c/( γB), the soil internal friction angle ϕ, and the horizontal seismic coefficient kh on the seismic bearing capacity are examined. In addition, the failure mechanisms are also discussed, and comparisons with previous studies of static nature are conducted.

Probabilistic stability analysis of qanat tunnels in c-φ soil considering soil spatial variability

Some newly built high-speed railways inevitably pass through the qanat region, which may potentially cause the failure of the qanat tunnels upon embankment and traffic loadings. Thus, it is of great importance to evaluate the stability of the qanat tunnels under surcharge for the design of railways. In the context of the Tehran–Isfahan railway construction in Iran, the soil properties obtained from a series of site investigation and laboratory tests show an important spatial variability. To better consider the spatial variability of soil strength parameters, a series of random adaptive finite element limit analysis (RAFELA) is performed in this study to investigate the stability of the qanat tunnels in the cohesive-frictional soils. The emphasis is placed on the effects of the coefficient of variation and vertical spatial correlation length of the strength parameters (i.e. soil cohesion c and effective fiction angle φ) and the qanat tunnel depth (H/D). Results show that considering the variabilities of both c and φ is more unfavourable to the qanat stability compared to the cases with only one strength parameter (c or φ) variability being considered. Detailed stability evaluation charts are obtained to assess the probability of failure of the qanat tunnels under different conditions.

Probabilistic risk assessment of earth dams with spatially variable soil properties using random adaptive finite element limit analysis

Probabilistic risk assessment of earth dams with spatially variable soil properties using random adaptive finite element limit analysis

Influence of copula approaches on reliability analysis of slope stability using random adaptive finite element limit analysis

AbstractRecently, random field copulas have been deployed to characterise the dependent structures of spatially variable soil parameters. This study expands on this concept by implementing finite element limit analysis (FELA) with adaptive meshing alongside the copula approach to perform reliability assessment of a geotechnical problem. A hypothetical slope with drained and undrained soil conditions was used as an example. First, adaptive FELA was carried out on the hypothetical slope. Second, single and multiple dependency soil parameter structures were represented by several selected copulas (Gaussian, Frank and Clayton). Finally, random adaptive FELA was implemented to explore the effects of copula selection on slope stability and reliability analyses. Results show that considerably different slope failure probabilities are produced by different copula approaches, and that failure probabilities reduce for simulating multiple dependency structures. In addition, failure probability exhibits different tendencies between drained and undrained soil conditions as soil parameter cross‐correlations become stronger. Failure probabilities are also different when performing lower and upper bound (UB) random adaptive FELA with each of the selected copulas.

Seismic Stability of Dual Tunnels in Cohesive–Frictional Soil Subjected to Surcharge Loading

In this study, a self-developed adaptive finite element limit analysis (AFELA) code was adopted to explore the stability of dual tunnels in cohesive–frictional soil subjected to surcharge loading and seismic action. Parametric studies of different influential factors, including the depth of tunnels, horizontal distance between tunnels, seismic acceleration coefficient, unit weight, cohesion and internal friction angle of soils, were conducted using the AFELA code. An adaptive meshing technique was adopted for optimal accuracy and efficiency, and a pseudostatic method was used to simulate the seismic action. Strict upper bound (UB) and lower bound (LB) results with relative errors of less than 7% were acquired. Detailed design tables were presented to facilitate the engineering design, and three typical failure patterns, including single side-wall failure, half-cross-shaped failure and cross-shaped failure, corresponding to different stable levels, were summarized for a deeper insight into how the failure mechanism evolved under different conditions. The results indicated that the variations in soil unit weight and void depth affected the seismic bearing capacity almost linearly. Furthermore, the dual tunnel system is vulnerable to seismic actions, and the stability of tunnels was further undermined by the adverse effects of additional seismic-caused interactions between two adjacent tunnels.

Stability Analysis of Deep Rectangular Tunnels Using Adaptive Finite Element Limit Analysis with Hoek–Brown Failure Criterion

The purpose of this study is to investigate the stability of deep rectangular tunnels excavated in a jointed rock mass using adaptive finite element limit analysis (AFELA) method. The rock mass is assumed to obey the generalized Hoek–Brown failure criterion. The numerical results from parametric studies are presented in the form of dimensionless tables and figures concerning stability numbers (Ns). Typical failure mechanisms are depicted and discussed based on visualized results from AFELA. The results demonstrate that Ns decreases with geological strength index (GSI), increases with disturbance factor (D), stays nearly unchanged with the intact rock yield parameter (mi) and is less sensitive to GSI as D decreases. Besides, an analytical upper bound limit analysis method is also applied to provide a check on the validity of the results from AFELA. The influence of the excavation-induced disturbance on the stability of deep rectangle tunnels is investigated by introducing a disturbance coefficient (ζ).

Undrained stability analysis of strip footings lying on circular voids with spatially random soil

Random adaptive finite element limit analysis (RAFELA) is introduced to investigate the stability of the footing-voids system with random soils. The emphasis of this study is, for the footing-void system, on quantifying the influence of spatial variability on its bearing capacity and the failure probability. Of particular interest is that random field theory is utilized to characterize the spatial variability of soil, and at the same time, failure probability is calculated by imposing Monte-Carlo simulations on independent cases. Strict close bearing capacity could be obtained within the scope embraced by upper bound (UB) results and lower bound (LB) results. By imposing the proposed modelling, comprehensive parametric studies were carried out, especially for the soil spatial correlation parameters and geometry parameters. The results indicated that the failure probability would increase with the farther distance between the void and the footing, the greater coefficient of variation (COV) and the smaller vertical correlation length. Detailed design tables were presented to assess potential failure probability under different conditions. Typical failure patterns are also summarized, revealing a positive correlation between the failure probability and the diffusion degree of failure curves.

Stability analysis of rock slopes using strength reduction adaptive finite element limit analysis

The main aim of this study is to propose an effective approach to conduct the stability analysis of rock slopes. Based on the strength reduction technology, the recent developed adaptive finite element limit analysis is adopted to investigate the stability of rock slopes for the first time. The rock mass strength is described by the latest generalized Hoek-Brown failure criterion. To better estimate the rock slope stability, the rock mass disturbance D and slope angle B are also incorporated into the determination of factor of safety by implementing the disturbance weighting factor s and the slope angle weighting factor fB, respectively. The factors of safety obtained from this study are validated by those from existing works based on two real slope cases. For practical use, the factors of safety for the cases of B=45o in undisturbed rock masses are provided in the form of design charts. Finally, a set of design charts for s and a fitting formula for fB are presented and discussed.

Seismic Bearing Capacity for Strip Footings on Undrained Clay with Voids

ABSTRACT This paper investigates the seismic bearing capacity of strip footings on undrained clay with single continuous square voids. Numerical studies for a wide range of geometric parameters and material properties are performed using adaptive finite element limit analysis (AFELA). Based on the pseudo-static approach, rigorous upper and lower bounds of the seismic bearing capacity for the strip footing are obtained, with relative errors of 4% or better. The calculated results are presented in the form of design tables and charts, and the effects of different governing parameters on the seismic bearing capacity are evaluated, including the size and location of the voids, the dimensionless strength ratio and the horizontal seismic coefficient. In addition, typical failure mechanisms are examined, and comparisons with previous studies are also conducted.

Undrained Seismic Stability of Dual Unsupported Circular Tunnels Subjected to Surcharge Loading

Undrained seismic stability of dual unsupported circular tunnels was investigated in this work using a self-developed code for adaptive finite element limit analysis. The so-called pseudo-static method was used to simulate the seismic effects during an earthquake. Accurate upper and lower bounds of seismic stability factor [Formula: see text] were obtained by using an adaptive remeshing technique incorporated in the code. Comprehensive parametric studies of the problem variables, including the horizontal seismic coefficient [Formula: see text], the relative spacing ratio [Formula: see text]/[Formula: see text], the relative depth ratio [Formula: see text]/[Formula: see text] and the strength ratio [Formula: see text]/[Formula: see text] were performed to provide dimensionless design tables for practical uses. In addition, visualized results from AFELA were summarized to reveal how the failure mechanism of dual tunnels would evolve with varying problems variables. Numerical results showed that both the stability and failure mechanism of dual tunnels can be much affected by seismic effects which should be carefully considered for a reasonable design in earthquake zones.

Stability of Unlined Rectangular Tunnels in Rock Masses Subjected to Surcharge Loading

Abstract This paper investigates the stability of unlined rectangular tunnels in rock masses subjected to surcharge loading using adaptive finite element limit analysis based on the generalized Hoe...

Stochastic analysis of dual tunnels in spatially random soil

The undrained stability of dual circular tunnels buried in spatially random soils is investigated by imposing the random adaptive finite element limit analysis (RAFELA). The emphasis is on quantifying the effect of influential factors including the geometry parameters and spatially variability parameters on the bearing capacity and failure probability of tunnels by assuming a lognormal distribution on undrained shear strength within a spatial correlation structure. Predictions were obtained by the scope enclosed by upper bound (UB) and lower bound results (LB) results within 5% relative errors. To account for a combined effect simultaneously caused by depths of tunnels, spaces between tunnels, soil weights, and spatially variability parameters on the stability of tunnels, all independent variables are involved in parametric studies in pairs. Results revealed several failure patterns and announced how the stability evolves with changes in tunnel geometry and soil spatial variability.

Characterization of the sinkhole failure mechanism induced by concealed cave: A case study

The formation of sinkholes in karst areas has become a dangerous geohazard over the last two decades and has been increasingly studied by researchers worldwide. A concealed karst cave caused a sinkhole failure event in Ziran village of Longyan City, Fujian Province, China (N25°44′20″, E117°21′99″) on 27 June 2015. A detailed field investigation showed that the failure event was induced by the enlargement of a concealed karst cave. A numerical model based on an adaptive finite element limit analysis was implemented to determine the failure mechanism and the affected regions of the sinkhole. The critical state, critical load and failure mechanism were directly analyzed using limit theorem analysis and the discrete finite element technique. The results demonstrate that the enlargement of karst caves by the suffosion effect of groundwater played an important role in karst collapse. Gravity is predicted to induce damage to a karst cave with a critical radius r of 1.25 m, thereby destabilizing the ground surface and resulting in the appearance of a sinkhole. This study provides reliable analysis methods for sinkholes caused by concealed karst caves and serves as a reference for preventing similar geohazards around the study area.