Finite Element Limit Analysis Research Articles

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.

Prediction of Undrained Lateral Capacity of Free-Head Rectangular Pile in Clay Using Finite Element Limit Analysis and Artificial Neural Network

Prediction of Undrained Lateral Capacity of Free-Head Rectangular Pile in Clay Using Finite Element Limit Analysis and Artificial Neural Network

Nonisothermal Failure Envelopes of Strip Shallow Foundations Resting on Partially Saturated Clay Subjected to Combined Inclined and Eccentric Loadings

Shallow foundations are commonly resting on partially saturated soil and are very likely to be exposed to severe variations of temperature. The degree of saturation and matric suction will be changed at the elevated temperatures, thus resulting in different hydromechanical behavior and a considerable variation in the imposed suction stress. In this study, the effect of temperature increase on the ultimate bearing capacity of strip shallow foundations resting on partially saturated clay layer subjected to vertical (V)–horizontal (H)–moment (M) combined loading is examined through a set of finite-element limit analyses (FELA) adopting lower bound theorems and second-order cone programming (SOCP). The unified effective stress for partially saturated soils is first incorporated into the soil yield function, considering the significant effect of temperature variations on suction stress by means of the well-established previously developed nonisothermal soil–water retention curve (SWRC) model. The equilibrium equations corresponding to the combined loading are also incorporated into the FELA formulations to account for the effects of inclined and eccentric loadings. Accordingly, the failure loci of obliquely and eccentrically loaded shallow foundations are presented for a wide range of temperatures. It is shown that with an increase of the temperature in the underlying unsaturated clay, the suction stress within the soil medium significantly rises, and thus, the failure wedges as well as the failure loci for both eccentric and inclined loadings substantially expand at elevated temperatures, revealing the considerably greater bearing capacity of the strip footing. The contact pressure beneath the foundation in all loading scenarios increases with an increase in the temperature of the underlying clay. This trend is much less pronounced at higher angles of load inclination, while it is barely affected by the load eccentricity. In addition, with an increase in the induced temperature and consequently the suction stress within the partially saturated clay beneath the foundation, the failure wedge expands, thereby resulting in an overall increase in the bearing capacity of the shallow foundation against vertical–horizontal–moment combined loading.

Support Pressure for Stability of Horseshoe-Shaped Tunnels in Undrained Clay Using Lower-Bound Finite-Element Limit Analysis

Support Pressure for Stability of Horseshoe-Shaped Tunnels in Undrained Clay Using Lower-Bound Finite-Element Limit Analysis

Development of an improved limit pressure equation for structurally distorted thin-walled pressurized 90 degree pipe bends

PurposeThis paper aims to present the approximate limit pressure solutions for thin-walled shape-imperfect 90° pipe bends. Limit pressure was determined by finite element (FE) limit analysis with the consideration of small geometry change effects.Design/methodology/approachThe limit pressure of 90° pipe bends with ovality and thinning has been evaluated by geometric linear FE approach. Internal pressure was applied to the inner surface of the FE pipe bend models. When von-Mises stress equals or just exceeds the yield strength of the material, the corresponding pressure was considered as the limit pressure for all models. The current FE methodology was evaluated by the theoretical solution which has been published in the literature.FindingsOvality and thinning produced a significant effect on thin-walled pipe bends. The ovality weakened pipe bend performance at any constant thinning, while thinning improved the performance of the bend portion at any constant ovality. The limit pressure of pipe bends under internal pressure increased with an increase in the bend ratio and decreased with an increase in the pipe ratio. With a simultaneous increment in bend radius and reduction in wall thickness, there was a reduction in limit pressure. A new closed-form empirical solution was proposed to evaluate limit pressure, which was validated with published experimental data.Originality/valueThe influences of structural deformation (ovality and thinning) in the limit pressure analysis of 90° pipe bends have not been investigated and reported.

Strength-based material layout optimization of solid reinforced concrete

Whether monetary, environmental, or otherwise, the cost of the structure is always an important aspect when designing reinforced concrete. A structure with a low cost is desirable, but other considerations must be made. First and foremost, the structures should be safe. The two conditions define the structural optimization problem that this paper seeks to solve as finding the structure with the lowest cost, which is also safe. Validation of reinforced concrete in the ultimate limit state is often performed using plasticity and strength-based methods. This paper combines Finite Element Limit Analysis (FELA) with a yield criterion that includes material layout variables to create a strength-based structural optimization framework for solid reinforced concrete structures. The yield criterion combines the Modified Mohr–Coulomb criterion, where variables scale the compressive strength, with the inclusion of smeared reinforcement, where variables scale the reinforcement ratios. The framework is presented and shown in examples using free optimization and examples where material layout variables in parts of the structure are coupled and optimized as a group.

Probabilistic seismic passive resistance of hunchback retaining wall considering spatial variability

The importance of gravity hunchback retaining wall in supporting a spatially random soil backfill subjected to earthquake is studied using probabilistic analysis. A lower bound finite element limit analysis formulation is used for plastic analysis of homogeneous and heterogeneous soil. The internal friction angle of soil is spatially varied using random field theory and Karhunen-Loéve expansion method. The uncertainty in soil parameter is recorded using Monte-Carlo Simulation method. The seismic waves are simulated using modified pseudo-dynamic approach. The effect of both inertial as well as body force on retaining wall and soil are considered. The behavior of soil at each time interval is studied and the most vulnerable behavior at a particular time is recorded for all cases of probabilistic analysis. The effect of depth of foundation soil is studied and observed that the analysis for a particular case with no foundation soil (i.e., rigid base) may overestimate the magnitude of passive resistance by around 2.3 times as compared to the wall with foundation soil. It is also worth noting that there are some cases of spatial variability where the probability of failure is non-zero due to soil heterogeneity even when the factor of safety is more than 1.5.

Influence of reinforcement design on seismic stability of full-height panel MSE walls

A numerical study was carried out to investigate the seismic stability of mechanically stabilized earth (MSE) walls using a finite element limit analysis (FELA) approach. The numerical method was validated using results from shaking table tests and limit equilibrium (LE) analysis. A series of parametric analyses was subsequently carried out to examine the influences of reinforcement design on seismic stability and failure mechanisms in full-height panel MSE walls. Results of the study indicate that, as opposed to the linear or bilinear failure mechanisms typically assumed in current design guidelines, more complex failure geometries could form in the backfills that involve extended reinforcement, which can be captured and analyzed using the FELA method employed in this study. The results also confirm the current consensus that placing longer reinforcement layers at the top of the wall (i.e. tapering-down arrangement) can help improve its seismic stability. However, in shorter walls or when high-strength reinforcement is used, a tapering-up reinforcement arrangement could also lead to increased seismic stability.

Stability Charts for Limiting Horizontal Normal Pressure on Cohesive-frictional Backfill for Deep Contiguous Piled Walls

Background: This study presents a numerical solution for determining the limiting uniform normal pressure acting horizontally behind cohesive-frictional backfill material in a deep contiguous piled wall. At this limiting pressure, the soil tends to flow out in gaps between a series of vertical piles placed at a certain uniform horizontal spacing. Methods: The lower and upper bound plane strain finite element limit analysis (FELA) has been carried out for this purpose. The Mohr-Coulomb failure criterion, using an associated flow rule, was employed to impose the yield condition in the soil mass. Results: A parametric study was carried out to obtain the magnitude of the non-dimensional limiting lateral resistance (F/cD) as a function of normalized pile spacing (S/D), the friction angle of soils (ϕ), and the adhesion factor (δ) at the soil-pile interface; here, F refers to the lateral normal resistance (force) per unit length offered by the pile, S forms the clear spacing between piles, D is the diameter of the pile and c is soil cohesion. The impact of the different parameters on the failure mechanisms has been examined comprehensively. Conclusion: The lateral resistance (F/cD) offered by the piles increases generally with a decrease in the spacing between the piles. The magnitude of F/cD increases further with an increase in the values of ϕ and δ.

Bearing capacity prediction of strip and ring footings embedded in layered sand

A prediction model for the bearing capacity estimation of strip and ring footing embedded in layered sand is proposed using soft computing approaches, namely, artificial neural network (ANN) and random forest regression (RFR). The required data for the model preparation were generated by performing lower- and upper-bound finite-elements limit analysis by varying the properties of the top and bottom layers. Two types of layered sand conditions are considered in the study: (a) dense on loose sand; (b) loose on dense sand. The investigation for strip footing was carried out by varying the thickness of the top layer, embedment depth of the foundation and friction angles of top and bottom layers. For a ring footing, the internal-to-external diameter ratio forms an additional variable. In total, 1222 and 4204 data sets were generated for strip and ring footings, respectively. The performance measures obtained during the training and testing phase suggest that the RFR model outperforms the ANN. Also, following the literature, an analytical model was developed to predict the bearing capacity of strip footing on layered sand. The ANN and the generated analytical model predictions agreed with the published experimental data in the literature.

Undrained trapdoor and tunnel face stability revisited

In this study, closed-form solutions are presented for two classical problems: the load exerted on strip or circular trapdoors and the stability of tunnel headings in purely cohesive soils, considering both the case of a constant undrained shear strength and of a linear vertical strength profile. The solutions are based on a minor modification of Gunn's lower-bound plasticity solution. According to comparative numerical stress analyses and finite-element limit analyses, the proposed equations accurately estimate trapdoor loads and face support pressures in soils with uniform strength, while they are slightly conservative in the case of depth-dependent shear strength. Thus, they are appropriate for the assessment of the stability of underground structures in saturated, low-permeability soils subjected to short-term loading and exhibiting depth-dependent strength – which, so far, has only been possible numerically.

Effect of eccentricity on ultimate lateral unit earth pressure of tetrapod piles in clay

This study investigates the ultimate lateral unit earth pressure of rigid tetrapod foundation imposed by eccentric loads, based on a couple of two-dimensional adaptive finite-element limit analyses with lower-bound, upper-bound and 15-node mixed Gauss element formulations. A parameter study is conducted to emphatically explore the influence of eccentricity as well as to assess the role of additional parameters such as soil–pile interface strength and pile spacing on the normalised lateral earth pressure factor Np. Results from the numerical analyses reflect that the presence of loading eccentricity may lead to significant reduction in lateral soil resistance, the maximum diminution is up to 45% for the case that eccentricity equals to 0·5 times spacing. Three representative failure mechanisms are identified associated with various eccentricities. Pile spacing and interface strength additionally affect the variation of failure mechanisms with eccentricity increases. Finally, the eccentricity reduction factor, defined as the ratio of the Np considering the effect of loading eccentricity to the Np omitting this effect, is proposed, and the variation of this factor with eccentricity is presented for different values of pile spacing and soil–pile adhesion factor.

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.

A generalised analytical framework for active earth pressure on retaining walls with narrow soil

Active earth pressure on retaining structures supporting a narrow column of soil cannot be properly analysed using Coulomb's theory. Finite-element limit analysis (FELA) shows that the soil forms multiple failure surfaces if the soil column is sufficiently narrow. This paper proposes a framework for active earth pressure estimation for narrow soils by combining an arched differential element method and a sliding wedge method. The analytical framework considers both soil friction and cohesion, soil arching effects and shear stress between adjacent differential elements. The solution obtained is validated against experimental data and FELA results. Through parametric studies, the effects on the active earth pressure of the aspect ratio, soil friction, soil cohesion and wall–soil interface roughness are examined. To facilitate the use of the proposed framework in design, a modified active earth pressure coefficient and an application height of active thrust are provided.

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.

In-situ investigation on coal mine overburden dump slope and its seismic stability considering heterogeneity

Stability of the coal mine overburden (OB) dump slopes is many times compromised owing to the lesser availability of the in-situ characteristics of the OB dump materials and their spatial heterogeneity. In this study, multi-channel analysis of surface waves (MASW) investigation was carried out for the characterization of OB dump materials of Jambad opencast coal mine of India and the variation of heterogeneous in-situ characteristics has been reported in terms of statistical parameters. Next, the stability of a two-bench OB dump slope against seismic forces was investigated through finite element limit analyses coupled with random field theory utilizing Karhunen-Loeve expansion method for the spatial heterogeneity of the OB dump material. The effects of spatial heterogeneity of the OB dump material on the probability of failure and the critical pseudostatic seismic coefficient of the slope were investigated through Monte-Carlo simulations. The influence of spatial heterogeneity of OB dump materials were investigated with both isotropic and anisotropic correlation lengths. Finally, seismic slope stability analyses were also carried out using the discrete element method for the size heterogeneity of the OB dump materials. This study summarizes the effects of heterogeneity of material property and size on the seismic stability of OB dump slope.

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

FELA investigation of eccentrically-loaded footing on parallel tunnels constructed in rock masses

The ultimate bearing capacity of an eccentrically loaded strip footing above twin square tunnels buried in rock masses was examined using the generalized Hoek-Brown (GHB) yield criteria. To get reliable findings, the stability assessments were carried out using finite element limit analysis (FELA) code in combination with a sophisticated adaptive remeshing approach. Case studies with two different tunnel layouts, parallel and symmetrical, were examined. Comprehensive parametric analyses were given to demonstrate the effect of load eccentricity, rock mass strength parameters, and tunnel position on the stability of the strip footing. The visualized results of the FELA programme were presented to show how the failure mechanism would change with different influential factors. Moreover, the results were validated by comparing them to earlier investigations.

Design Equations for Predicting Stability of Unlined Horseshoe Tunnels in Rock Masses

This paper aims to propose new stability equations for the design of shallow, unlined horseshoe tunnels in rock masses. The computational framework of the upper- and lower-bound finite-element limit analysis is used to numerically derive the stability solutions of this problems using the Hoek–Brown failure criterion. Five dimensionless parameters including the width ratio and the cover-depth ratio of the tunnels, as well as the normalized uniaxial compressive strength, the geological strength index, and the yield parameters of the Hoek–Brown rock masses, are considered in the study. Selected failure mechanisms of the horseshoe tunnels in rock masses are presented to portray the effect of all dimensionless parameters. New design equations for stability analyses of horseshoe tunnels are developed using the technique of nonlinear regression analysis and the average bound solutions. The proposed stability equations are highly accurate and can be used with great confidence by practitioners.

Data-Driven Prediction of Stability of Rock Tunnel Heading: An Application of Machine Learning Models

In this paper, Artificial Neural Networks (ANN) have been utilized to predict the stability of a planar tunnel heading in rock mass based on the well-defined Hoek-Brown (HB) yield criterion. The HB model was developed to capture the failure criterion of rock masses. To provide the datasets for an ANN model, the numerical upper bound (UB) and lower bound (LB) solutions obtained from the finite element limit analysis (FELA) with the HB failure criterion for the problem of tunnel headings are derived. The sensitivity analysis of all influencing parameters on the stability of rock tunnel heading is then performed on the developed ANN model. The proposed solutions will enhance the dependability and preciseness of predicting the stability of rock tunnel heading. Note that the effect of the unlined length ratio has not been explored previously but has been found to be of critical importance and significantly contributes to the failure of rock tunnel heading. By utilizing the machine learning-aided prediction capability of the ANN approach, the numerical solutions of the stability of tunnel heading can be accurately predicted, which is better than the use of the classic linear regression approach. Thus, providing a better and much safer assessment of mining or relatively long-wall tunnels in rock masses.