Finite Limit Research Articles

Stability analysis of multiple unsupported excavations in cohesive-frictional soils using finite element limit analysis (FELA) and an artificial neural network (ANN)

Stability analysis of multiple unsupported excavations in cohesive-frictional soils using finite element limit analysis (FELA) and an artificial neural network (ANN)

Working platforms and bearing capacity assessments of sand overlying clay using finite element limit analysis

The bearing capacity of shallow foundations on layered soils is typically based on empirical models assuming a strip footing. Shape factors are then applied to the strip footing solution to account for the specific geometry of the foundation being considered. A common practical application of this methodology is when the ultimate bearing capacity of a granular working platform constructed over a clay subgrade is estimated using the Working Platforms for Tracked Plant BRE-470 guideline. Previous studies using finite element limit analysis have been undertaken to examine a strip footing on a layered soil and how the resulting bearing capacity compares to that derived from BRE-470. This paper presents an extension of previous work by the authors using finite element limit analysis to investigate the three-dimensional influence on the bearing capacity of square and rectangular footings on sand over clay. The finite element limit analysis solutions are used to produce charts to assist designers with estimating the ultimate bearing capacity of granular working platforms overlying clay. The paper also aims to highlight some important considerations when adopting the BRE-470 guideline to design granular working platforms overlying clay.

Two-species k-body embedded Gaussian unitary ensembles: q-normal form of the eigenvalue density

The eigenvalue density generated by an embedded Gaussian unitary ensemble with k-body interactions for two-species (say π and ν ) fermion systems is investigated by deriving formulas for the lowest six moments. Assumed in constructing this ensemble, called EGUE(), is that the π fermions (m 1 in number) occupy N 1 number of degenerate single particle (sp) states, and similarly the ν fermions (m 2 in number) occupy N 2 number of degenerate sp states. The Hamiltonian is assumed to be k-body preserving . Formulas with finite corrections and asymptotic limit formulas both show that the eigenvalue density takes q-normal form with the q parameter defined by the fourth moment. The EGUE() formalism and results are extended to two-species boson systems. The results in this work show that the q-normal form of the eigenvalue density established only recently for identical fermion and boson systems extends to two-species fermion and boson systems.

Revisiting Active and Passive Earth Pressure Problems using Three Stability Factors

This paper presents rigorous plasticity solutions to the classical active and passive earth pressure problems. The primary method adopted is a conventional equation based on the soil property and three stability factors (Fc, Fs, and Fγ), that are analogous to Terzaghi’s bearing capacity factors (Nc, Ns, and Nγ) of strip footings. The proposed method is considered as a practical yet smart approach to the determination of earth pressures and is one of the main novelties in this study. To achieve this, the finite element limit analysis (FELA) of upper and lower bounds solutions, a powerful tool in studying the behaviour of soil stability, is employed to compute the three stability factors for a wide range of soil internal friction angles, wall roughness, and surcharge pressures. In addition, analytical solutions based on statistically admissible stress fields are adopted to validate the proposed FELA solutions. The validation satisfactorily demonstrated the accuracy and reliability of the proposed solutions. It follows that the numerical results are presented in the form of tables, figures, and several examples provided to demonstrate the practical use of the three factors in estimating active and passive earth pressures with various backfill soils, wall roughness, and surcharge pressure. The study should, therefore, be of value to practitioners.

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

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

A nonlinear programming algorithm for finite element limit analysis using feasible arc searching technique

AbstractThis article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length; (ii) the avoidance of solving an additional “phase one problem” for finding an initial feasible point; and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces.

Structural Limits of Orbital Compliance and Treatment Options for Pathologic Orbital Pressure.

The integrity of the orbit has a finite structural limit due to the compliance of its tissue. The authors investigate these limits to quantify them and inform the treatment of heightened ocular and orbital pressure. Cadaveric study with 12 orbits being volumized before randomization of treatment for pathologic levels of ocular and orbital pressure. First-line and second-line treatment was chosen randomly (lateral cantholysis, superior septolysis, inferior septolysis). Prior to treatment, IOP, orbital compartment pressure, and axial globe projection was measured after delivery of each 1cc aliquot and surgical treatment. Orbital compartment pressure and IOP were well correlated (r = 0.99). The average reduction in IOP after treatment averaged a 56.2 mm Hg reduction in IOP. All treatments were statistically equivalent ( p < 0.01). Loss of compliance (P LOC ) was determined when the mean plus 1 standard deviation of change in IOP/ml volume was achieved with simultaneous change in exophthalmometry of <0.5 mm change/ml added volume, indicating an acceleration in pressure in the face of a steady volume. This criteria was met for 11 of 12 orbits. The 12th orbit missed this threshold by 1 mm Hg in IOP. P LOC occurred at an average IOP of 43.0 mm Hg (±5.8 mm Hg, 90% CI) and after an average injection of 13 ml (±1.4 mm, 90% CI). Additionally, lateral cantholysis, superior septolysis, and inferior septolysis were statistically equivalent in reducing IOP after P LOC . IOP and orbital compartment pressure are excellent proxies for each other in the authors' model. Orbital compliance is a mathematic phenomenon that can be quantified, as evident in this investigation. P LOC can inform timing for orbital decompressions in the presence of heightened IOP. Multiple procedures can be used to extinguish dangerously high orbital compartment pressure.

Nonlinear coherent structures of nucleus-acoustic wave excitations in multi-nuclei quantum plasmas with ultra-relativistically degenerate electrons and positrons

The propagation dynamics of the nucleus-acoustic waves (NAW) in a quantum plasma composed of nondegenerate inertial light nuclei, stationary heavy nuclei, and ultra-relativistically degenerate electrons and positrons has been theoretically investigated within the framework of the Boussinesq equation, which is valid for a bi-directional propagation of a small but finite amplitude limit. The N-soliton solution of the Boussinesq equation is derived using Hirota's method. It is found that positive potential structures exist in the sonic and supersonic regimes, whereas negative potential structures are found to be present in the subsonic regime. Pertinent plasma properties are analyzed for one-, two-, and three-soliton solutions in terms of different parameters. In addition to the typical solitary wave solutions, our findings indicate that the nonlinear NAW has breather structures. The three- and four-soliton solutions are used to construct the elastic interaction solutions of the breather–soliton and breather–breather, respectively. The findings are discussed in the context of ultra-relativistic astrophysical plasmas.

New failure mechanism for evaluating ultimate inclined load adjacent to slope.

A new failure mechanism is proposed for calculating the ultimate inclined load adjacent to the slope, i.e., the slope is in the limit state when the critical slope contour and the slope surface are at the critical position where two intersections will occur. The conventional view is that the critical slope contour calculated by the method of characteristics has only a concave shape. This study found that the critical slope contour changes from concave to convex when the inclined load imposed on the slope top surface increases. The feasibility of the proposed method is verified by the finite element limit analysis (FELA) and the definition of the ultimate load. The parametric analysis showed that the current method of characteristics (CMOC) overestimated the ultimate inclined load and gave an incorrect conclusion since it assumed larger failure models at a low strength ratio or large friction angle. The proposed method does not require assumption or search of the failure models, and it can solve the shortcomings of CMOC.

Finite elements limit analysis formulation using the power type yield criterion for plane strain and axisymmetric stability problems

The current research employs a power type yield criterion which accounts for the dependency of the shear strength parameters, namely, cohesion and internal friction, on stress level which becomes quite effective in obtaining very accurately the solutions of different stability problems in geomechanics involving soil and rock media. The present manuscript introduces plane strain and axisymmetric formulations which deal with the power type yield criterion and are based on the lower and upper bound finite elements limit analysis in conjunction with the power cone programming (PCP). To demonstrate the efficacy of the proposed formulations, the problems of the determination of the bearing capacity of strip and circular foundations in a cohesive-frictional soil medium have been addressed. In the case of a strip footing, the earthquake inertial forces in a horizontal direction have also been incorporated. The adaptive mesh pattern has been employed to improve the accuracy of the solution at the expense of minimal computational effort. The results have been thoroughly validated by making the comparison of the obtained solutions with that reported in literature. The proposed formulations are expected to be quite useful in solving different stability problems in geomechanics.

Seismic Bearing Capacity of Strip Footings Placed Adjacent to Rock Slopes

ABSTRACT The bearing capacity of strip footings placed adjacent to the rock slopes subjected to pseudo-static horizontal earthquake body forces has been investigated by using the upper bound (UB) finite element limit analysis (FELA) in combination with a mesh adaptive strategy. The generalized Hoek–Brown (GHB) failure criterion is applied to describe the strength properties of rock masses, which can be treated as its native form without the smoothing of the yield surface while employing the second-order cone and power cone programming to solve the optimization models. Based on the UB FELA method, the seismic bearing capacity factor is determined considering the effect of different governing parameters, namely the horizontal earthquake acceleration coefficient k h , the normalized slope height H/B, the rock strength ratio σ ci /γB, the geological strength index GSI and the material constant m i . For design purpose, a series of non-dimensional charts are provided, and typical failure mechanisms are also discussed in detail.

Pullout capacity of vertical plate anchors in unsaturated clay considering variable surface flow conditions

Vertical plate anchors are placed in the soil to improve the lateral resistance of various geotechnical structures. Extensive research has been conducted to find out the pullout capacity of vertical anchors in saturated or dry soil. Despite all these attempts, no research is available to study the behavior of anchors in unsaturated soil where the shearing resistance of soil is governed by the matric suction depending on the surface flow conditions and water table positions. Since the soil in field is mostly in unsaturated state; thus, the pullout resistance of vertical plate anchor has been aimed to be evaluated in this study. Finite element limit analysis solutions in terms of a non-dimensional pullout factor have been presented to find the pullout capacity of vertical anchors. The solutions are inclusive of the effect of soil properties, embedment depth, height of anchor plate, depth of water table from the ground surface, flow conditions and flow rate under an immediate breakaway condition. The effect of variation of other factors like the degree of saturation, unit weight of soil, van-Genuchten SWRC parameters, specific gravity of soil solids, and anchor-soil interface conditions has also been evaluated.

Effect of surface crack and undercut on the stability of cliff

By considering the modeling advantages of the lower bound finite element limit analysis (LBFELA), the present study introduces a novel and simple technique to analyze the influence of an existing surface crack on the stability of cliff having an undercut. By incorporating the different boundary conditions along the discontinuity edges, two types of existing cracks, i.e., fine and separated, are considered. The rock mass at collapse is modeled as the Generalized Hoek-Brown failure criterion with the help of power cone programming (PCP) in the self-developed LBFELA code. The variation in stability caused by the presence of both types of surface crack and undercut is presented in terms of a stability number, σci/γH; where σci represents the uniaxial compressive strength of rock sample, γ is the unit weight of the rock mass, and H is the height of cliff. The variation in the magnitudes of σci/γH is presented as design charts by considering the different depths of surface crack and the various strength parameters of rock mass. The reduction of stability is observed in the presence of surface crack and undercut. As expected, in the presence of a separated surface crack, lower stability is found in comparison with the presence of a fine surface crack on cliff. In addition, the prediction equations for the obtained stability number are presented by using both the classification and regression techniques with the help of artificial neural network (ANN). Furthermore, a sensitivity analysis is performed, and it is found that H/vu and GSI are the most sensitive parameters among all the input parameters. Failure patterns are also studied to find the extent of the plastic state during the collapse.

Stability evaluation of elliptical tunnels in natural clays by integrating FELA and ANN

The stability of tunnels in clayey soil is a major concern for underground space technology. Clay has anisotropy in shear strength induced by depositional and sedimentation processes. For the numerical analysis of geotechnical stability problems, the anisotropic undrained shear (AUS) model can account for this anisotropy of clayey soils. In this study, the stability of the elliptical tunnel (stability factor: σs-σt/suc) with varying elliptical shape (width-depth ratio: B/D) placed at different embedment depths (cover-depth ratio: C/D) in clay with different anisotropy (anisotropic strength ratio: re) and varying dimensionless overburden factor (overburden factor: γD/suc) is evaluated using finite element limit analysis and the AUS model. The failure planes are also evaluated for the above variations. Based on the numerical outcome, the artificial neural network (ANN) is utilized to establish the equation for predicting the stability of the elliptical shape tunnel with different shapes (i.e., width-depth ratio), and varying overburden, cover-depth ratio, varying anisotropic strength ratio of clay. The present study results are presented as design charts, tables, and equations so that they can be used in practice.

A Sterling Look at Stirling’s Constant

Summary In a previous article [3] appearing in this journal, existence of the finite positive limit implicit in Stirling’s approximation was proved, and in so doing this limit was connected to the Euler limit . Because it was not done in the original article, exact determination of the constant () by a novel, elementary technique is the aim of this follow-up. For both articles, the arguments are readily accessible to advanced undergraduate students with a year of university calculus in their background.

Force-induced fluorescence spectrum shift of spiropyran-based polymer for mechano-response sensing

As spiropyran exhibits mechanophore response, i.e., becomes vibrantly fluorescent under an applied force, its change has been measured primarily by fluorescence intensity. However, fluorescence intensity, which is an extensive property, is strongly affected by specimen and set-up parameters, and the corresponding measurements therefore require laborious and assumptive corrections. Herein, spiropyran is covalently linked to poly(dimethylsiloxane) and an in-situ opto-mechanical set-up is developed to monitor fluorescence spectrum evolution under deformation. Peak wavelength, which is an intensive property, is shown to be a superior mechano-response indicator that offers high accuracy/reliability, allows one to establish a 1:1 correspondence to strain (or stress) without corrections, and is independent of size. To the best of our knowledge, this is the first report of peak wavelength as mechano-response indicator for SP and its first systematic in-situ study. In summary, peak wavelength is shown to successfully reflect the force applied to polymer specimens without the need for corrections and exhibit considerable resistance to cycling-induced fatigue, while analysis of the finite extensibility limit reveals that the change of peak wavelength is closely related to the forces exerted directly on the polymer chain.

Ultimate bearing capacity of strip footings above rectangular voids in Hoek-Brown rock masses

The bearing capacity of a rigid strip footing placed on a rock mass with a rectangular void is determined using the upper bound finite element limit analysis in conjunction with the adaptive mesh refinement technique. The rock mass is assumed to obey the generalized Hoek-Brown (GHB) yield criterion. The optimization model is solved by using the second order cone and power cone programming, which enables the GHB yield criterion to be used in its native form, without the need for smoothing. Based on the method, the reduction factor is calculated and presented in a series of dimensionless charts for design purpose. The influence of material parameters (such as the geological strength index GSI, material constant mi and intact rock strength σci) and geometric parameters (including the height and width of the void, as well as the horizontal and vertical distance between the void and the strip footing) on the reduction factor is considered. Typical failure patterns are discussed in detail to offer a deeper explanation of how the voids affect the bearing capacity of strip footing.

FELA evaluation of undrained bearing capacity of cutting edge of circular open caisson

ABSTRACT Circular open caissons are deep foundations sunk into the ground utilising the self-weight of cutting edge and steining as driving force along with the subsequent failure of soil in bearing. During the sinking of the caisson, the clay in contact with the cutting edge is subjected to undrained loading and the controlled sinking of the caisson can be achieved by evaluating the undrained bearing capacity of the cutting edge. In the study, the undrained bearing capacity factor (N) of the cutting edge for varying cutting angle (b), radius ratio of the caisson (r i /r o ), full embedment of the caisson (d), removal of soil within the caisson (d'), and different roughness (α) conditions of the steining are evaluated using finite element limit analysis (FELA). The factors affecting the undrained stability of caisson considering all practical scenarios are addressed and presented as charts to be used in practice.

Mechanisms for the Formation of an Exceptionally Gently Inclined Basal Shear Zone of a Landslide in Glacial Sediments—The Ludoialm Case Study

The Ludoialm landslide, which is located in the municipality of Münster in Tyrol, Austria, represents a large-scale translational landslide in glacial soil sediments characterised by an exceptionally low inclined basal shear zone of only 12°. Although a temporal coincidence between meteorological events and slope displacement is obvious, the hydromechanical coupled processes responsible for the initial landslide formation and the ongoing movement characteristics have not yet been identified. This article provides a comprehensive analysis of the predisposition factors and the initial failure mechanism of this landslide from geological and geotechnical perspectives. We use a prefailure geometry of the cross section to simulate the initial slope failure process by a limit equilibrium analysis (LEA), a strength-reduction finite element method (SRFEM), and a finite element limit analysis (FELA). The shape and location of the computationally obtained basal sliding zone compare well with the geologically assumed one. Based on the computational study, it turns out that a high groundwater table probably caused by snow melting in combination with different permeabilities for the different layers is needed for the formation of the exceptionally low inclined basal shear zone. This paper presents the failure mechanism of the Ludoialm landslide and discusses the role of the shear band propagation in the process of slope destabilization.

Bearing capacity of shallow strip foundations on reinforced soil subjected to combined loading using upper bound theorem of finite element limit analysis and second-order cone programming

Bearing capacity of shallow strip foundations placed over both unreinforced and reinforced granular soils and subjected to combined loading is calculated by implementation of upper bound finite element limit analysis in conjunction with second-order cone programming technique. The soil mass is considered to be a granular medium reinforced with the inclusion of horizontal single and double layers of geogrid elements. To represent the impact of tensile resistance of reinforcement elements, an axillary variable is utilized to simulate the plastic energy dissipation of reinforcing elements without the application of any stress variables. General loading conditions are considered to profile the expansion of the failure envelopes in the V-H and V-M spaces for shallow strip foundations resting on reinforced soils. Results of this study are compared and validated against three different cases including the bearing capacity of shallow strip foundations subjected to vertical loading in the case of perfectly smooth and fully rough interfaces, limit load of shallow strip foundations subjected to combined loading, and vertical bearing capacity of shallow strip footings over a soil deposit reinforced with a single-layer of geosynthetic. Consistency of the results with those reported in the literature demonstrates the efficiency of proposed extended finite element upper bound formulations. The results are reported in the form of an efficiency factor which can be multiplied by the vertical bearing capacity of the shallow strip footing over unreinforced soil to find the ultimate bearing capacity of the reinforced foundation. The results show that the load inclination angle and eccentricity have significant impacts on the limit load and the optimum embedment depths of the reinforcement layer. It is further noted that the effect of reinforcement layer(s) in the improvement of bearing capacity in the V-M space is more pronounced than in the V-H space. The efficiency of reinforcement elements inclusion in improving the expanse of safe loading domain in the V-H and V-M spaces enhances with an increase in the soil internal friction angle.