Finite Element Limit Analysis Research Articles

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.

Combined bearing capacity of footings on geogrid-reinforced granular fill over soft clay

The current study investigates the ultimate bearing capacity of obliquely/eccentrically loaded shallow strip foundations resting on a geogrid-reinforced granular fill with limited thickness over a very soft to soft clay layer. To this end, the lower bound theorems of the finite element limit analysis (FELA) and second-order cone programming (SOCP) are effectively exploited to simulate the underlying clay deposit, geogrid layer, and granular fill along with the inclined/eccentric loading exerted on the overlying footing. The accuracy of the adopted formulations is rigorously examined through several comparisons with the results of a well-established analytical approach in the literature. A comprehensive parametric study is then conducted to properly examine the influences of the geosynthetic layer characteristics and soft clay properties on the overall bearing capacity and failure envelope of the strip footing subjected to wide ranges of inclined and eccentric loadings. The results show that placement of a geogrid-reinforced granular fill layer over the soft clayey soil significantly increases the bearing capacity of the shallow foundation. The ultimate tensile strength of the reinforcement layer and the cohesion of the underlying very soft to soft clay deposit are also observed to have considerable effects on the size of failure envelopes.

Centrifuge and analytical modeling of counterweight retaining walls under translation mode

Counterweight retaining walls (CRWs) are a variant of gravity-retaining walls that feature a pressure relief platform (RP) on the backfill side to reduce total earth pressure, offering a cost-effective option compared to traditional forms. However, the intricate interactions between CRWs and backfill, coupled with the lack of clear design guidelines, have restricted their use. This study examines the behavior of CRWs in translation mode using three different centrifuge model tests, each with varying fill heights. Observations show a slightly concave slip surface through the wall heel and a nearly planar slip surface extending from the edge of the RP to the back of the wall in an active limit state. Backfill movement can be classified into translation, sliding, and stable zones. Earth pressure distribution on the upper wall follows a trapezoidal pattern, whereas the pressure on the lower wall exhibits a triangular distribution. Earth pressure on the RP is approximately linear, peaking near the RP’s edge. Introducing a friction angle mobilization factor for the potential first slip surface improves accuracy in calculating earth pressure. The tests were replicated to validate the analytical model for earth pressure calculations, using the adaptive finite-element limit analysis method.

Machine learning approaches for stability prediction of rectangular tunnels in natural clays based on MLP and RBF neural networks

In underground space technology, the issue of tunnel stability is a fundamental concern that significantly causes catastrophe. Owing to sedimentation and deposition processes, the strengths of clays are anisotropic, where the magnitudes of undrained shear strengths in the vertical and horizontal directions are different. The anisotropic undrained shear (AUS) model is effective at considering the anisotropy of clayey soils when analyzing geotechnical stability issues. This study aims to assess the stability of rectangular tunnels by adjusting the dimensionless overburden factor, cover-depth ratio, and width-depth ratio in clay with various anisotropic strength ratios. The stability analysis of these tunnels involves employing finite element limit analysis and the AUS model to identify the planes of soil collapse in response to the aforementioned variations. In addition, this study presents the development of soft-computing models utilizing artificial neural networks (ANNs) to forecast the stability of rectangular tunnels across various combinations of input parameters. The findings of this study are presented in the form of design charts, tables, and soft-computing models to facilitate practical applications.

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.

Application of artificial neural networks for predicting lateral and uplift capacity of buried rectangular box carrying pipelines

Urban and offshore subterranean comprehensive pipelines are currently utilized frequently as infrastructure for fitting different engineering pipelines used for electricity, signal transmission, natural gas, petroleum, heating, water supply, and drainage systems. This study utilizes the finite element limit analysis (FELA) and artificial neural network (ANN) to evaluate the pull-out capacity factor of the buried rectangular box carrying the pipelines with internal inclined force in cohesive soil. In FELA, rigorous upper bound and lower bound solutions are performed to achieve the exact result. In this study, a dimensionless parametric analysis is carried out by considering the effect of five parameters viz. buried depth ratio, width-depth ratio, overburden factor, internal inclination angles, and interface factor on the pull-out capacity factor of a buried rectangular box, which can be called as a rectangular pipeline. Two significant samples of the investigated parameters are selected to evaluate the soil failure pattern (failure envelope) using the shear dissipation of soil failure for the buried rectangular pipeline subjected to inclined loading. Using the FELA results, the predictive equations are proposed using ANN, and then sensitivity analysis is performed to examine the sensitivity of each investigated essential parameter on the stability of the underground rectangular pipeline. The predictive ANN model for the buried rectangular pipe subjected to inclined loading is presented as design charts for practice and further investigation.

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.

Effect of strain-softening and strength anisotropy on the undrained bearing capacity of non-associated clay

The bearing capacity of soils is critical in the design and analysis of foundations. The classical solutions derived from methods of characteristics and bound theories are based on the rigid plasticity and associated flow rule, which may not be realistic for natural soils. The undrained shear strength of soft clays exhibits strain-softening and anisotropic behaviour in laboratory tests, which creates complexity when choosing appropriate strength parameters in the conventional design process. In addition, the stress–strain characters are non-associative and path dependent, which also affects the bearing capacity of soils. This paper investigates two classical stability problems (i.e. deeply embedded pile/pipe section and rigid strip footing) using finite-element analysis and the MIT-E3 soil model, and demonstrates the effects of stain-softening and strength anisotropy on the undrained bearing capacity of soils. The computed results are compared with analytical solutions and finite-element limit analyses, as well as those from finite-element analysis using conventional soil models. These findings have strong practical implications in predicting the bearing capacity of foundations and interpreting in situ tests.

Stability analysis of a vertical excavation reinforced with horizontal nails using three-dimensional finite elements limit analysis

Three-dimensional stability analysis of a vertical excavation, reinforced with grouted horizontal nails, has been carried out by using the three dimensional lower and upper bounds based finite elements limit analysis (FELA) using Optum G3. The nail along with the surrounding grouted cementitious material is assumed to behave as a single monolithic cylindrical block which was assumed to be either rigid or an elasto-plastic material following the Von-Mises yield criterion. The excavation is assumed to fail on account of either an interface shear slippage between nails and surrounding soil mass or on an account of axial tensile rupture of the composite nail material for a few typical cases as well. The soil unit weight has been varied to induce the ultimate shear failure of the soil nailed excavation. The unit weight of the soil mass at which the failure of the nailed wall occurs is termed as γcr. Two different types of boundary conditions along the base of the excavation have been considered. In the first case, the in-situ soil mass behind the excavation is extended below the base as well (Case 1) and in the second case, the excavation is assumed to simply lie on a hard stratum (Case 2). The results have been provided in the form of a non-dimensional stability number N=γcrHc as a function of soil friction angle φ, Sv/H, SH/H, d/H, L/H and m; where H refers to height of the wall, d is diameter of the grouted nail, Sv and SH imply centre to centre vertical and horizontal spacing of the nails, and m is the mobilization factor between grouted nails and adjoining soil mass. The results from the analysis have been found to compare well with the data reported in literature. All the results have been presented in the form of non-dimensional stability charts, which will be useful for design for any given values of height H and cohesion c. From the observed failure mechanisms, an analysis has also been carried out to determine the optimized lengths of nails. The optimized lengths of nails for both Cases 1 and 2 have been also provided. The type of failure mechanism, base or face failure, dictates the optimized lengths of the nails.

Advanced Finite Element Limit Analysis and Machine Learning for Assessing the Stability of Square Tunnels in Rock Slope

Advanced Finite Element Limit Analysis and Machine Learning for Assessing the Stability of Square Tunnels in Rock Slope