Finite Element Limit Analysis Research Articles

Stability Factors F c , F s , and F γ for Twin Tunnels in Three Dimensions

This paper aims to study the three-dimensional (3D) tunnel heading pressure of twin circular tunnels in a drained cohesive–frictional soil using a stability factor approach and finite-element limit analysis (FELA). The primary concept adopted will be the use of a conventional equation that is similar to the traditional bearing capacity factors (e.g., Nc, Ns, and Nγ) in Terzaghi’s bearing capacity equation. For various spacing ratios (S/D) between the tunnels, the stability of the tunnels is expressed in terms of nondimensional tunnel stability factors (e.g., Fc, Fs, and Fγ), which are functions of the depth ratio (C/D) and soil internal friction angle (ϕ). For conciseness, the results will be presented in charts and tables with the tunnel stability factors that used the rigorous FELA upper (UB) and lower bound (LB) solutions.

Limit Analyses of the Active Earth Pressure on Rigid Retaining Walls under Strip Loading on Backfills

Recent studies of retaining walls include experimental studies, numerical analysis and analytical models. Although active earth pressure against retaining structures has received much attention, the evaluation of active earth pressure of backfill when loaded by a strip foundation, has been slightly studied. This paper studies the effect of a strip load on the active pressure force and the distribution of the horizontal stresses on a rigid wall, using a finite element limit analysis. The strip loading is located at different distances from the vertical face of the wall. The OptumG2 code is used to analyze the effect of width of strip surcharge (soil-wall), interface friction angle and soil internal friction angle. New interesting results are demonstrated and presented here: the dependency of the active earth pressure coefficient on both position and width of the strip load, in one hand, and the effect of the internal friction angle of the soil, the soil-wall interface, and the position of the strip loading on the failure mechanism, in the other hand.

Application of Artificial Neural Networks for Predicting the Stability of Rectangular Tunnels in Hoek–Brown Rock Masses

An artificial neural network (ANN) model for predicting the stability of rectangular tunnels in rock masses based on the Hoek–Brown (HB) failure criterion is presented in this study. Since the safety assessment of the tunnel stability is one critical issue for civil engineers during the construction, it is very important to develop a reliable and accurate stability analysis of such problems. The finite element limit analysis (FELA) with the HB failure criterion is used to develop the numerical upper and lower bound solutions of the problem of rectangular tunnels in rock masses. A novel machine learning-aided prediction of this problem is then developed based on the datasets of the numerical bound solutions obtained from the FELA. The inputs consist of six dimensionless parameters including the cover-depth ratio of tunnels, the width ratio of tunnels, the normalized uniaxial compressive strength, the geological strength index, the mi parameter, and the degree of disturbance of rock masses. The results show that the optimal ANN models provide very great accuracy in predicting the stability of the rectangular tunnels based on the HB failure criterion. The solutions will provide a prompt assessment of tunnel stability in rock masses for geotechnical engineers during the construction of rock tunnels.

Stability Charts for Closely Spaced Strip Footings on Hoek–Brown Rock Mass

Footings are constructed closely to each other in mountainous rock areas and the determination of closely spaced bearing capacity footings on rock masses has become an important topic of recent research. The primary aim of this paper is to determine an efficiency factor, just like in the design of a pile group, that can be used to evaluate the bearing capacity of closely spaced footings on Hoek–Brown mass. The advanced finite element limit analysis of upper and lower bound theorems is used to study the stability of two and multiple interfering footings using the Hoek–Brown parameters such as GSI (geological strength index) and mi (Hoek–Brown yield parameter). This study found that the efficiency factor is influenced by three dimensionless parameters including GSI, mi, and S/B. Failure mechanisms of the problems are also investigated, and stability charts and tables produced for practical uses. Overall, these results broadly support the common understanding of the two key parameters GSI and mi in the HB failure criterion. As a result of these investigations, suggestions were identified for future research.

Modelling of Critical Acceleration for Regional Seismic Landslide Hazard Assessments by Finite Element Limit Analysis

The critical acceleration model plays an important role in seismic slope stability and determines the predictive accuracy of regional seismic landslide hazard assessments. Recently, the critical acceleration model based on the limit equilibrium method has been used to evaluate the seismic stability of regional slopes. However, when the Hoek-Brown failure criterion is used to evaluate the seismic stability of slopes with angles greater than 60°, the results obtained is unconservative by limit equilibrium method. Therefore, based on the simulation of a typical slope model with finite element limit analysis, prediction equations of the critical acceleration are established. The corresponding results are compared with the prediction results from the limit equilibrium method. This comparison shows that the proposed critical acceleration model has higher predictive accuracy than the limit equilibrium method, especially when the Hoek-Brown failure criterion is used to evaluate the slopes with angles greater than 60°. The proposed model is applicable to the global scope and can be effectively applied to regional seismic landslide hazard assessments.

Probabilistic failure envelopes of strip foundations on soils with non-stationary characteristics of undrained shear strength

This paper investigates probabilistic failure envelopes of strip foundations on spatially variable soils with profiles of undrained shear strength, su, linearly increasing with depth using lower-bound random finite-element limit analysis. The spatially variable suis characterised by a non-stationary random field with linearly increasing mean and constant coefficient of variation (COV) with depth. The deterministic uniaxial capacities and failure envelopes are first derived to validate the numerical models and provide a reference for the subsequent probabilistic analysis. Results indicate that the random field parameters COVsu(the COV of su) and Δ (dimensionless autocorrelation distance) have a considerable effect on the probabilistic normalised uniaxial capacities, which alters the size of the probabilistic failure envelopes. However, an insignificant effect of COVsuand Δ on the shape of probabilistic failure envelopes is observed in the V–H, V–M and H–M loading spaces, such that failure envelopes for different soil variabilities can be simply scaled by the uniaxial capacities. In contrast to COVsuand Δ, the soil strength heterogeneity index κ = μkB/μsu0has the lowest effect on the probabilistic normalised uniaxial capacity factors, but the highest effect on the shape of the probabilistic failure envelopes. A series of expressions is proposed to describe the shape of deterministic and probabilistic failure envelopes for strip foundations under combined vertical, horizontal and moment (V–H–M) loading.

Bearing capacity of open caissons embedded in sand

Open caissons are an increasingly common means of constructing underground storage and attenuation tanks as well as launch and reception shafts for tunnel-boring machines. The caisson walls typically feature a tapered base, referred to as the ‘cutting face’, to aid the sinking process by reducing the vertical soil reaction. The primary aim of this paper is to explore the influence of the caisson cutting face inclination angle on the vertical soil reaction in sand. Both finite-element limit analysis and finite-element analysis are adopted for this purpose. The effects of cutting face roughness, external embedment depth and caisson radius are also investigated. The results show that the influence of the cutting face inclination angle on the bearing capacity is highly dependent on both the soil friction angle and the roughness of the cutting face. A reduction in the caisson radius is also shown to cause a significant increase in the vertical soil reaction. The numerical output is used to inform the development of a new closed-form analytical approach amenable for use in routine design. The design method is shown to provide a high-fidelity representation of the numerical output.

Lower bound limit analysis for an axisymmetric problem in rock mass using power cone programming

AbstractBy using the lower bound finite elements limit analysis (LB‐FELA) and the power cone programming (PCP), a methodology has been introduced to solve an axisymmetric stability problem with the usage of the generalized Hoek and Brown (GHB) yield criterion‐ applicable for rock mass. The formulation involves the application of the GHB yield criterion in its native form without any smoothing and it does not require any assumption associated with the circumferential stress (σθ). The efficacy of the proposed formulation in a rock mass has been demonstrated by determining (i) the bearing capacity of a circular footing, (ii) the stability numbers for an unsupported vertical cylindrical excavation, and (iii) the vertical uplift capacity of a circular horizontal anchor. The obtained solutions have been compared with that reported in literature. Failure patterns for each problem have also been explored. For the anchor problem, for no solution is reported with the usage of the GHB criterion, the influences of different material yield parameters (GSI, mi, and σci), unit weight of rock mass (γ), and the embedment ratio (H/B) of the anchor on the uplift capacity have been comprehensively examined.

Seismic Stability of the Slope Containing a Laterally Loaded Pile by Finite-Element Limit Analysis

In this study, the seismic stability of a slope containing a laterally loaded pile under seismic conditions is evaluated by the finite-element limit analysis (FELA) approach. The seismic action is idealized as a horizontal seismic coefficient, ranging from 0 to 0.3, within the framework of the pseudo-static approach, and applied as an accelerogram of earthquakes to the numerical model in the seismic analysis. By means of the adaptive meshing technique, the finite-element method, and limit theorem of plasticity, the slope failure mechanism need not be presumed in advance. The feasibility of the FELA is validated by comparing the obtained factors of safety and critical sliding surfaces with those provided by published literature. Based on this, the effects of various factors (e.g., horizontal seismic coefficient, internal friction angle, cohesion, slope angle, slope height, and lateral load atop the pile) on the factor of safety and failure mechanism, with a normalized parameter (seismic-multiplier) is proposed. Furthermore, some detailed design tables and four representative slope failure patterns are presented to estimate the seismic stability of the slope containing a laterally loaded pile.

Stability Assessment of Rock Mass System under Multiple Adjacent Structures

Numerical modeling is important for exploring the fundamental processes occurring in rock and for evaluating the real performance of structures built on and in rock mass system, and thus for supporting the design of rock engineering problems. Estimating the stability of rock mass foundation systems entirely based on a theoretical approach is a complicated task if there exists overlapping of their potential collapse modes. This paper applies finite element limit analysis to evaluate the bearing capacity of equally spaced multiple strip footings resting on rock mass obeying the modified non-linear Hoek–Brown failure criterion. Numerical solutions are expressed in terms of the efficiency factor that is dependent on the spacing between footings, as well as the rock mass properties. In addition, the effects of surface surcharge and footing roughness are quantified. The maximum spacing at which the interfering effect of adjacent footings becomes disappeared is evaluated and an algebraic expression for approximating the maximum spacing is proposed. Failure mechanisms for a few cases of rock mass under multiple strip footings are examined.

3D stability analysis of unsupported rectangular excavation under pseudo-static seismic body force

ABSTRACT In this paper, the seismic stability number of unsupported excavations in cohesive-frictional soil under the influence of pseudo-static seismic body forces is examined. Three-dimensional finite element limit analysis is employed to numerically solve the upper and lower bounded models of unsupported excavations. The results are represented by a dimensionless stability number which is a function of four dimensionless parameters including the excavation aspect ratio, the excavated depth ratio, the soil’s effective friction angle, and the coefficient of horizontal earthquake acceleration. For the first time in literature, the influences of a soil’s effective friction angle and the coefficient of horizontal earthquake acceleration on the mechanisms of excavation failures are examined and discussed. Also presented is a case study to demonstrate the use of the proposed seismic stability number in studying unsupported excavations in seismic risk areas.

Seismic vertical uplift capacity of horizontal strip anchors embedded in sand adjacent to slopes using finite element limit analysis

Seismic vertical uplift capacity of horizontal strip anchors embedded in sand adjacent to slopes using finite element limit analysis

Bearing capacity of single stone column in clay using finite element limit analysis

Stone columns are used as an efficient ground improvement technique, which could increase the bearing capacity of native soft soil, reduce settlement, increase rate of consolidation and mitigate liquefaction potential. In this study, the finite element limit analysis (FELA) with the adaptive mesh, including both upper bound and lower bound approaches, was applied for prediction of ultimate bearing capacity of single stone column. It was observed that a critical slenderness ratio exists in which the failure mechanism changes from punching to bulging. An equation was derived for prediction of the critical slenderness ratio as a function of cohesion of the native clayey soil and friction angle of the stone column. A two-criteria equation is also presented to predict the ultimate bearing capacity of single stone column under both punching and bulging mechanisms. Moreover, the effect of footing roughness on the ultimate bearing capacity of the stone column was investigated. It was observed that the influence of footing roughness is more significant for bulging-type failure. The results of this study are also compared with some of the previously published analyses in the literature.

Limit analysis solutions for stability factor of unsupported conical slopes in clays with heterogeneity and anisotropy

The novel stability solutions of unsupported conical slope in anisotropic and inhomogeneous clays utilizing the lower-bound (LB) and upper-bound (UB) finite-element limit analyses (FELA) are proposed in this paper. The anisotropic undrained shear (AUS) model and linear increasing undrained shear strength are employed to determine the anisotropic and inhomogeneous soil behavior, respectively. The stability factor [Formula: see text] is obtained with the variations of dimensionless parameters including the ratio of anisotropic ([Formula: see text], the rate of increasing undrained shear strength ([Formula: see text], the ratio between the height and the radius at the bottom slope ([Formula: see text]/[Formula: see text], and the inclination angle of slope ([Formula: see text] provided in sample charts. The failure patterns of conical slope considering the affected parameters are also obtained and described.

Efficiency of various mitigation schemes in the alleviation of the destructive effect of reverse dip-slip fault rupture on surface and embedded shallow foundations using upper bound finite element limit analysis

It is attempted in this study to alleviate the destructive influences of rigid foundation-fault rupture interaction using various mitigation schemes. The efficiency of such mitigation techniques to divert the mainstream of the fault rupture from overlying superstructures is examined through a comprehensive set of limit analysis simulations using the upper bound theorem along with finite elements discretization and linear programming.The accuracy of this novel numerical analysis developed for the simulation of the interaction between fault and foundation is rigorously validated against various high-quality experimental studies throughout the literature. Consecutively, an extensive parametric survey is carried out on the geometric and strength properties of seismic wall barriers to meticulously explore their efficacy on the diminution of the deformation of the shallow foundation subjected to the emergence of reverse dip-slip fault rupture outcrop at the ground surface. Accordingly, the influences of all effective variables related to the mitigating wall, including the wall depth, width and relative position, and also its material type (EPS geofoam, soil-bentonite and LECA) and the corresponding strength properties, on the fault-foundation interaction are thoroughly examined. The results showed that the increase in the fault throw leads to a significant augmentation of the foundation rotation for all unprotected and protected cases under study.

Estimation of the Critical Seismic Acceleration for Three-Dimensional Rock Slopes

An analytical approach for the estimating of critical seismic acceleration of rock slopes was proposed in this study. Based on the 3D horn failure model, the critical seismic acceleration coefficient of rock slopes was conducted with the modified Hoek–Brown (MHB) failure criterion in the framework of upper-bound theory for the first time. The nonlinear Hoek–Brown failure criterion is incorporated into the three-dimensional rotational failure mechanism, and a generalized tangent technique is introduced and employed to convert the nonlinear Hoek–Brown failure criterion into a linear criterion. The critical seismic acceleration coefficients obtained from this study were validated by the numerical simulation results based on finite element limit analysis. The agreement showed that the proposed method is effective. Finally, design charts were provided for exceptional cases for practical use in rock engineering.

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.

Investigations of a Weathered and Closely Jointed Rock Slope Failure Using Back Analyses

This study presents the case of a landslide triggered by a high groundwater level caused by several days of continuous rainfall in the northeastern region of Taiwan. The slope where this landslide occurred consists of closely jointed and weathered bedrock. By means of finite element limit analysis and the Hoek–Brown failure criterion, this study performed a slope failure simulation similar to the actual landslide and deduced the reasonable value range for the combination of key Hoek–Brown failure criterion parameters through back analyses. The results indicate that the key parameters affecting the bedrock’s slope stability were the geological strength index (GSI) and the disturbance factor (D), whereas the effects of the unconfined compressive strength (σci) were less significant. The results of the back analysis reveal that the suitable D-value range and GSI of closely jointed and weathered sandstone in the northeastern region of Taiwan are 0.8 to 0.9 and 20 to 30, respectively. These back-analyzed value ranges can serve as a reference for broader applications in the preliminary stability analysis of similar rock slopes where it is difficult to perform in situ investigation.

Homogenization based kinematic limit analysis for finding the stability of an embankment over soft clay reinforced with granular columns

The present study examines the stability of an embankment of cohesive-frictional material placed over a purely cohesive stratum which is reinforced by means of uniformly spaced vertical granular cylindrical columns. By using the kinematic yield homogenization concept, the macroscopic yield strength envelope associated with the reinforced clay layer has been obtained numerically for different volumetric fractions of the granular column to the composite unit cell by using the semidefinite programming (SDP) technique. An upper bound approximation of the macroscopic yield criterion, using the least square method, is expressed as a summation of a number of convex ellipsoidal envelopes so that the solution for computing the stability factors for the embankment on granular column (in the presence of surcharge pressure) can be obtained later with the usage of the second order cone programming (SOCP) while performing the upper bound finite elements limit analysis. The methodology avoids the usage of any stress variable and the complete procedure has been clearly described and the associated code has been written in MATLAB. The study will be not only useful for designing embankments constructed over soft clay reinforced with granular columns but also for solving different geomechanics stability problems by using the homogenization based kinematic limit analysis approach.

Hybrid Framework for Forecasting Circular Excavation Collapse: Combining Physics-Based and Data-Driven Modeling

The use of supporting fluids to stabilize excavations is a common technique adopted in the construction industry. Rapid detection of incipient collapse for deep excavations and timely decision making are crucial to ensure safety during construction. This paper explores a hybrid framework for forecasting the collapse of fluid-supported circular excavations by combining physics-based and data-driven modeling. Finite-element limit analysis is first used to develop a numerical database of stability numbers for both unsupported and fluid-supported circular excavations. The parameters considered in the modeling include excavation geometry, soil strength profile, and support fluid properties. A data-driven algorithm is used to learn the numerical results to develop a fast surrogate amenable for integration within real-time monitoring systems. By way of example, the proposed forecasting strategy is retrospectively applied to a recent field monitoring case history where the observational method is used to update the input parameters of the data-driven surrogate.