Finite Element Limit Analysis Method Research Articles

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.

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.

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 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.

Effect of single and dual voids on vertical capacity of large-diameter monopiles in marine clay

This study utilizes the finite element limit analysis (FELA) method to numerically investigate the effect of single and dual voids on the vertical bearing capacity of nearshore large-diameter monopiles in marine clay. After validating the numerical model, numerous numerical analyses in predicting the behavior of the pile-void system were conducted under different geometric parameters of pile and void, different pile-void distances, and different undrained shear strengths. These numerical results can be expressed in the form of design charts for vertical capacity reduction coefficients, which can facilitate a quick and straightforward assessment of pile capacity considering single and dual voids by multiplying the capacity without voids by respective coefficients. In addition, the numerical results can further give the contours of the plastic multiplier of the pile-void system which can be used to graphically conclude several representative failure modes. In short, this study intuitively illustrates the void effect on the pile vertical bearing capacity (including failure mode) and shows the significant differences between the cases with single and dual voids.

Structural stability of lunar lava tubes with consideration of variable cross-section geometry

This paper provides detailed numerical analyses of lunar lava tubes stability, where for the first time variability in cross-section geometries is considered. A novel approach included a dedicated procedure for extracting characteristics needed for random geometry generation together with the demonstration of its usage. Stability analyses were performed with finite element limit analysis (FELA) which is found to be very effective for analyzing tens of thousands of realizations. The FELA method provides collapse geometries that were examined to constrain the relations between the collapse size extent and width of the lava tube. New findings on types and sizes of lunar lava tube roof collapses were obtained, and they are the first step toward making stability analysis more realistic for future human and robotic exploration of lunar lava tubes. The results allow us to constrain the approximate widths of the lunar tube beneath skylights to be 300 m, as observed for the assumed rock parameters. In addition, the probabilistically based analyses allow to show that thin roofs (< 10 m) are very unlikely to be stable for the tubes of a few hundred meters in width under lunar conditions, and that the gravity trigger failures are more probable on the Moon when considering variations in lava tube geometry than for the previously considered cases of elliptical and circular shapes.

Stability analysis for excavation in frictional soils based on upper bound method

This paper adopted both the numerical and analytical methods to investigate the excavation stability against base heave failure. The finite element limit analysis method (OPTUM) was firstly employed to calculate the safety factor of the excavation stability against base heave failure, and the failure mechanism of the excavation was obtained. Based on the analysis and observation of the numerical results, a rigid block rotational failure mechanism was proposed, and the analytical formula of the safety factor of the excavation was developed through the upper bound method of limit analysis. In order to verify the rationality of the proposed failure mechanism, the analytical formula of the safety factor and the failure pattern of excavation were compared with the numerical results and the existing classical failure mechanism. Furthermore, the influences of soil and excavation conditions on the excavation stability were analyzed and discussed. Finally, a rigid block rotational failure mechanism under stratified stratum conditions was also proposed to consider effects of the complex soil conditions on the excavation stability. The results show that the proposed rigid block rotational failure mechanism provides a more critical safety factor calculation result for actual engineering examples and obtains a more continuous and smooth failure surface, which can serve as an alternative for the analytical method of excavation stability.

Three-dimensional seismic face stability of shield tunnels in undrained clay

Tunnel face stability has received increasing research interest over the past few decades. However, computing time-efficient and safe three-dimensional solutions under seismic loading is still an unsolved problem, while case studies indicate that seismic loading can be one critical destabilizing factor affecting tunnel stability. The primary objective of this work is to fill this gap in knowledge by providing compromising and computationally efficient solutions, along with their respective lower and upper bounds, to compute face stability under seismic conditions. The analyses employ the finite element limit analysis method to evaluate the limit support pressure in undrained clay, considering horizontal pseudo-static seismic forces pointing outwards from the face. Moreover, the analyses employ both constant and linearly increasing shear strengths with depth. The results are summarized as dimensionless stability charts and tables to facilitate their interpretation and future use for tunnel design. A new design equation has been developed to evaluate the stability of the tunnel face considering the effect of seismic forces. Additionally, the effects of different parameters on the shape of the failure mechanism have been investigated by analysing the distribution of shear dissipation.

Effect of single and dual voids on lateral capacity of large-diameter monopiles in marine clay

This study numerically examines the effect of single and dual voids on the lateral bearing capacity of nearshore large-diameter monopiles in marine clay by the finite element limit analysis (FELA) method. The ability of the numerical model to accurately predict the pile-void system behavior is evaluated by performing degenerated verification analyses on existing studies. Based on numerous numerical results, several design charts for capacity reduction coefficients are produced to provide a quick and straightforward assessment of the pile capacity with single and dual voids by multiplying that without voids by coefficients. Particularly, the coupling coefficient is further proposed to quantify the coupling effect between dual voids, and the corresponding design charts are also given. The subsequent parametric studies indicate that the void effect gets aggravated as the void is enlarged and close to piles but would be weakened as the soil around the pile gets strengthened; the void effect is positively and negatively associated with the void depth in the cases of low and great shear strength, respectively. The effect of single and dual voids (inc. coupling effect between dual voids) on the pile capacity and failure mode is further graphically explained by the plastic multiplier contour maps.

Stability Analysis of the Foundation Pit and the Twin Shield Tunnels during Adjacent Construction

Due to the rapid development of urban rail transit and the development and use of underground space, foundation pit construction near existing subway tunnels is becoming increasingly common. When adjacent foundation pit projects are being constructed, it is difficult to avoid the influence on existing subway tunnels, which threatens the safe operation of subway tunnels. Thus, this study focused on the stability of the adjacent construction of foundation pits and twin shield tunnels. The finite element limit analysis (FELA) method was used to analyze the influences of construction scheme and relative position of the twin shield tunnels and adjacent foundation pit on the global stability of adjacent construction. Based on the research results, the guidance and design for the construction scheme and relative position are provided. The stability analysis on the foundation pit during the construction process is performed. The criteria of adjacent influential partition are proposed, and the influence of various input parameters (c/γD, φ, L/D and C/D) on the global stability of adjacent construction is discussed, respectively. A new design equation of safety factor of global stability of adjacent construction is obtained by curve fitting.

Analyses on face stability of shallow tunnel considering different constitutive models

Based on the finite element limit analysis method, the stability of the face in case of active failure under three constitutive models, the Mohr-Coulomb model (MC), the modified Cambridge model (MCC) and the Drucker-Prager model (DP), were analyzed. The ultimate support pressure of the face and the influence of factors such as different burial depth ratios (C/D), cohesion (c) and friction angle (φ) in the MC model are also discussed. The results show that the safety factor obtained by the MCC model under the same support pressure is always smaller than that of the MC model, and the difference is the largest when there is no support pressure. As the support pressure increases, it will gradually approach the MC model. When the support pressure is small, the safety factor obtained by the DP model is larger than the MC model, but when the support pressure is large, it is smaller than the MC model, and the final difference tends to be stable. It is necessary to select an appropriate constitutive model according to different rock masses in practical engineering. The self-stabilizing performance of the face is not affected by C/D, and the ultimate support pressure will increase with the increase of C/D, decrease linearly with the increase of cohesion, and decrease with the increase of friction angle. When the friction angle is small, the ultimate support pressure is greatly affected by C/D, and when the friction angle is large, it is hardly affected by C/D.

Effect of slope on lateral bearing capacity of nearshore large-diameter monopiles in cohesive soil

This study investigates the effect of slope on the lateral bearing capacity of nearshore large-diameter monopiles in cohesive soil by the finite element limit analysis (FELA) method. The reduction coefficient is introduced to quantify the capacity reduction due to the slope effect, and the critical distance making the slope-induced capacity reduction negligible is normalized for generalization. After the validations by cases of different soils, an alternative way to quickly and straightforwardly assess the pile bearing capacity in sloping stratum for the most frequently-encountered cases in engineering practice is provided by multiplying the reduction coefficients in several design tables with the capacity in level stratum. The subsequent parametric studies indicate that the reduction coefficient and critical dimensionless distance are mainly governed by the internal friction angle, slope angle, and pile embedded length-diameter ratio but are almost insensitive to dimensionless cohesion and slope height-pile embedded length ratio. In addition, the failure mode of the pile-slope system would develop from local failure to transitional failure and global failure with a significant drop in pile bearing capacity while the pile-slope parameters cannot guarantee slope stability.

Effect of nearby strip loading on lateral capacity of offshore large-diameter monopiles in clay slope

This study is devoted to investigating the effect of nearby strip loading on the lateral bearing capacity of offshore large-diameter monopiles at the crest of marine clay slope by the finite element limit analysis (FELA) method. After the successive validations by cases of rigid piles and strip footings at the clay slope crest, the safe domains for the laterally loaded large-diameter monopiles are defined by the failure envelopes relating the dimensionless lateral bearing capacity H u/(c u D 2) to dimensionless strip loading q/c u. Particularly, all failure envelopes are depicted by closed-form expressions and design charts can then be given for a quick and straightforward assessment of dimensionless lateral bearing capacity for a wide range of frequently-encountered cases. In addition, the interaction between the pile bearing capacity and nearby strip loading is characterized by introducing the relationship of normalized parameters H u/(c u D 2) and q/c u, then graphically explained by plastic multiplier contour plots. Several kinds of representative curves are given successively to further clarify the effects of dimensionless factors on the interaction.

Finite element limit analysis of load-bearing performance of reinforced slopes using a non-associated flow rule

This paper presents a numerical study on the load-bearing performance of reinforced slopes under footing load using a finite element limit analysis (FELA) method where a non-associated flow rule is assumed in the analysis. The method was validated against results from full-scale model tests and a limit equilibrium (LE) analytical method. A series of parametric analyses was subsequently carried out to examine the influences that the soil dilation angle, footing location, and reinforcement design (i.e. length, tensile strength, and vertical spacing) could have on the load-bearing performance of reinforced slopes. Results indicate that dilation angle has a significant influence on the predicted magnitudes of bearing capacity, slope deformation, and mobilized reinforcement load. The predicted values of bearing capacity using the FELA are smaller than those from the Meyerhof's analytical method for unreinforced semi-infinite foundation, especially for larger friction angle values. Additionally, the ultimate bearing capacity of the slope and its corresponding horizontal deformation increase with the reinforcement tensile strength. Finally, the slip planes under the applied footing load are found to be y-shaped and primarily occur in the upper half of the slope.

Slip-Line Solution to Earth Pressure of Narrow Backfill against Retaining Walls on Yielding Foundations

When a retaining wall is adjacent to a natural slope, the overturning of the wall is usually caused by a yielding foundation. At the point of overturning, the narrow backfill behind the wall has reached the active limit state. However, in previous studies, the foundation conditions of the retaining wall were not fully considered when the earth pressure on the retaining wall with the narrow backfill was calculated. To comprehensively consider the stress state of the retaining wall, the finite-element limit analysis method was employed to study the failure mode of a retaining wall adjacent to a natural slope. The simulation results indicate that the sliding surface starts from the wall heel, with one side developing at the surface of the natural slope and the other developing in the ground in front of the wall. Based on this failure mechanism, a slip-line computational model for the retaining wall was established. When the slip-line solution was compared with the finite-element solution, the results were in good agreement. The plastic zone of the soil was determined by the slip-line field. In addition, the slip-line solution gave the active earth pressure of the narrow backfill, the passive earth pressure of the soil in front of the wall, and the foundation bearing capacity. Moreover, several extensive parametric studies were conducted. Thus, the shape of the narrow backfill, the rough soil–wall interface, and the low-strength backfill are all conducive to reducing active earth pressure on a retaining wall.

Topology optimization of truss structure considering nodal stability and local buckling stability

In order to obtain stable and realistic truss structures in practical applications, it is essential to include nodal and local buckling stability in truss topology optimization. There have been several approaches to address the challenges including nodal stability or local buckling stability. However, these approaches often lead to ill-conditioned optimization problems, such as convergence problems due to the concavity of the problem or high computational costs. In this study, two novel but conceptually simple methodologies, the nominal perturbing force (NPF) approach, and the allowable stress iteration (ASI) approach, are proposed to address nodal instability and local buckling instability problems in truss topology optimization, respectively. Initially, in the NPF approach, an infinite number of disturbing forces that a node may suffer are incorporated into the truss topology optimization problem in the form of nominal perturbing force conditions, whose magnitude and direction are discussed to capture the worst case. In the ASI approach, the allowable stress for each compressive bar is redefined in each iteration to ensure that the Euler critical buckling constraint is active. In this way, the concave local buckling instability problem is linearized in each iteration and can be solved efficiently by a linear programming solver. Finally, based on the finite element limit analysis (FELA) method, a truss topology optimization formulation incorporating the NPF and ASI approaches is proposed to solve the nodal stability and local buckling stability problems simultaneously. The proposed formulation is demonstrated through several numerical examples showing significant effects of including nodal stability and local buckling stability in the optimized designs, while at the same time demonstrating the validity and potential of the proposed approaches.

Effect of loading eccentricity on the ultimate lateral resistance of twin-piles in clay

This paper studies the effect of loading eccentricity and pile spacing on the ultimate lateral soil resistance of twin-piles using finite element limit analysis and analytical upper bound plasticity methods. Two kinematic mechanisms corresponding to the failure modes produced by the advanced finite element simulations are postulated with different eccentricity and pile spacing cases. Comparisons have shown excellent agreements between the two approaches. A series of parametric studies are then subsequently performed. Numerical results have shown that loading eccentricity considerably affects ultimate lateral soil resistance, leading to a maximum reduction of 50%. In addition, the curve of normalised pile resistance versus pile spacing ratio is dissimilar to that without considering the effect of loading eccentricity. The proposed solutions and failure mechanisms in this study will provide a deepened insight on the performance of twin-pile group under eccentric loads.

Investigations of Silty Soil Slopes under Unsaturated Conditions Based on Strength Reduction Finite Element and Limit Analysis

Matric suction plays a key role in slope stability by conferring an apparent cohesion component to the unsaturated portion of the soil. This paper adopts the total cohesion method to investigate the contribution of apparent cohesion on the stability of silty slopes under hydrostatic conditions. Phase2 and Optum G2 numerical programs, based on strength reduction finite element analysis and finite element limit analysis methods, respectively, are used for numerical analysis. Generally, Phase2 and Optum G2 results are in good agreement with each other. Optum G2 yields slightly higher factor of safety results than Phase2, particularly for steep slopes β≥ 30°. The results are presented in form of stability charts which are validated with a case from a previous study. Notably, the contribution of apparent cohesion to unsaturated shear strength is most pronounced when varying the water table. An examination of the slope failure mechanism reveals that the toe failure mechanism is the dominant failure mechanism. The depth of the failure surface is most sensitive to changes in the slope angle, cohesion and water table position. The influence of the air-entry value on the depth of the failure surface is contingent upon the location of the water table.

Finite element limit analysis of bearing capacity of footing on back-to-back reinforced soil retaining walls

The paper presents a numerical modeling study on the upper-bound bearing capacity of footing on back-to-back-Mechanically Stabilized Earth (MSE) walls using the finite element limit analysis (FELA) method. Numerical simulations were validated against results from other numerical simulation studies. Parametric analyses were carried out subsequently to examine the influences that the distance between reinforced zones, wall height, reinforcement design, and footing width and location could have on predicted bearing capacity and failure mechanism of back-to-back MSE walls. Results indicate that the influence of wall height on bearing capacity decreases with wall height. Additionally, a vertical slip plane could form along the back of reinforced zone in walls with tight reinforcement if the footing toe is located on the top of the retained zone. Finally, using a full-length top reinforcement layer (as opposed to lower-level layers) to connect the back-to-back walls is the most effective method to improve the bearing capacity of the structure subjected to footing load.

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).