Bound Theorem Research Articles

Shear friction response of lightweight concrete using bottom ash aggregates and air foams

ABSTRACT This study aimed to estimate the shear friction response of lightweight concrete made using bottom ash aggregates and air foam (LWC-BF) and determine the design parameters including shear transfer capacity, cohesion, and friction angle of such concrete at different interface conditions. The shear friction parameters were straightforwardly formulated from the extension version of the integrated mechanical models derived in our previous study based on the upper bound theorem of concrete plasticity. Eighteen non-reinforced push-off specimens (nine monolithic interfaces and nine interfaces with smooth construction joints) were tested under direct shear and the additional compressive stresses normally applied to the interfaces. The test parameters considered in different interface conditions were the compressive strength of concrete and the magnitude of compressive stresses. The experimental and analytical results showed that the addition of air foam slightly decreases the angle of friction of monolithic interfaces but insignificantly affects that of smooth construction joints. Thus, the effect of air foam added up to 20% by volume on the cohesion and friction angle of concrete was marginal. Therefore, the proposed shear friction parameters are promising to reasonably assess the shear friction strength of LWC-BF interfaces.

The Upper Bound Theorem in Forging Processes: Model of Triangular Rigid Zones on Parts with Horizontal Symmetry

This paper presents the analytical method capacity of the upper bound theorem, under modular approach, to extend its application possibilities. Traditionally, this method has been applied in forging processes, considering plane strain condition and parts with double symmetry configuration. However, in this study, the double symmetry is eliminated by means of a fluency plane whose position comes from the center of mass calculated. The study of the load required to ensure the plastic deformation will be focus on the profile of the part, independently on both sides of the fluence plane, modifying the number and the shape of the modules that form the two halves in which the part is defined. This way, it is possible to calculate the necessary load to cause the plastic deformation, whatever its geometric profile.

On the number of simplices required to triangulate a Lie group

We estimate the number of simplices required for triangulations of compact Lie groups. As in the previous work [11], our approach combines the estimation of the number of vertices by means of the covering type via a cohomological argument from [10], and application of the recent versions of the Lower Bound Theorem of combinatorial topology. For the exceptional Lie groups, we present a complete calculation using the description of their cohomology rings given by the first and third authors. For the infinite series of classical Lie groups of growing dimension d, we estimate the growth rate of number of simplices of the highest dimension, which extends to the case of simplices of (fixed) codimension d−i.

How many simplices are needed to triangulate a Grassmannian?

In this paper we use recently developed methods to compute a lower bound for the number of simplices that are needed to triangulate the Grassmann manifold $\G_k(\mathbb{R}^n)$. We first estimate the number of vertices that are needed for such a triangulation by giving a general lower bound and some more precise bounds for $k=2,3,4$. By applying the Lower Bound Theorem (LBT) of Barnette for triangulated manifolds, we then obtain estimates for the number of simplices in all dimensions. For higher-dimensional simplices these estimates can be considerably improved by using the recent progress on the Generalized Lower Bound Theorem for triangulated manifolds, which states that the $h''$-numbers of triangulated manifolds are unimodal, together with the computation of the Poincare polynomial. For example, we are able to prove that the number of top-dimensional simplices in a triangulation of $\G_k(\mathbb{R}^n)$ grows exponentially with $n$. Our method can be used to estimate the minimal size of triangulations for other spaces, like Lie groups, flag manifolds, Stiefel manifolds etc.

Seismic stability of three-dimensional slopes considering the nonlinearity of soils

Slopes are often unstable in adverse natural conditions, especially when suffering from seismic hazards. Due to the fact that conventional pseudostatic method fails to consider the dynamic properties of seismic waves, a pseudodynamic approach is adopted to characterize the seismic acceleration which varies with time and space. According to the upper bound theorem of limit analysis, an alternative strategy that slices the failure blocks in the horizontal direction to consider the spatial variations of seismic waves is proposed. Moreover, to consider the nonlinearity of the soil strength parameters, a tangential technique is used to capture the equivalent Mohr-Coulomb (M − C) parameters to obtain the least upper bound solution. The factor of safety (FOS) of the slope is implicitly restricted in the work balance equation established by the limit analysis upper-bound method with respect to a three-dimensional (3D) rotational mechanism. With the aid of the strength reduction technique, the least FOS can be eventually derived. By comparing to the pseudostatic method to the existing solutions, the validity and rationality of the proposed method is proven. A parametric study is carried out to reveal the influence of dynamic factors and nonlinear strength parameters on the safety of a slope.

Upper bound shakedown analysis of foundations on cohesive-frictional soil based on a nonlinear programming method

In this paper, using the upper bound shakedown theorem by means of the displacement finite element method and nonlinear programming, a numerical method is proposed to obtain the shakedown limit of strip footing under repeated loading. Shakedown analysis is a powerful method that provides the possibility to determine the shakedown limit of a structure. The shakedown limit of a structure under repeated loading is a load limit below which the structure is in the safe zone and its behaviour is elastic. For cohesive-frictional soil, the Mohr-Coulomb yield criterion is considered without any linearization. The role of the unit weight of the soil in the shakedown limit of a footing under repeated load is studied. Also, the effect of repeated load on the reduction of the bearing capacity of footing is investigated in several examples.

The penetration resistance of the elliptical tip of torpedo anchors in cohesive soil

Torpedo anchors are a new type of deep ocean anchor with a commonly elliptical anchor tip. However, little attention has been paid to theoretical research on the collapse load of the elliptical tip of the torpedo anchor. The lower and upper bound theorems are used to evaluate the penetration resistance of the anchor tip. A comparative analysis of the bearing capacity factor between the plastic limit solutions and the results presented in previous references is performed, and the feasibility of the lower and upper bound models is verified. As the aspect ratio of the anchor tip increases, the friction factor significantly affects the bearing capacity factor: the bearing capacity factor decreases with increasing the aspect ratio for smooth interface but increases with increasing the aspect ratio for the rough interface. Extended shape correction factors are obtained from the plane strain and axial symmetry results of the finite element method: 1.61 for a smooth interface, and 1.64 for a rough interface.

Three-Dimensional Lower and Upper Bound Analyses of Pile Systems

Abstract The objective of this paper is to present simplified methods for determining the three-dimensional (3D) system capacities of pile foundations based on the lower and upper bound theorems of...

Seismic Bearing Capacity of Rough Strip Footing Placed Over Geogrid-Reinforced Two-Layer Sands

Abstract The lower bound limit theorem in conjunction with finite elements is used to quantitatively estimate the pseudostatic bearing capacity of a rough strip footing placed on geogrid-reinforced...

A Calculation Method for Safety Distance Between the Confined Karst Cave and the Shield Tunnel Based on Upper Bound Theorem

A Calculation Method for Safety Distance Between the Confined Karst Cave and the Shield Tunnel Based on Upper Bound Theorem

The upper bound shakedown analysis of strip footing on cohesive slopes under repeated vertical–horizontal loads

Many foundations, such as those of industrial equipment, offshore structures and wind turbines, have to operate under repeated loads. Shakedown analysis is a powerful method that yields a straightforward calculation of a load limit below which the foundation will be stable under repeated loading. In this article, using the upper bound shakedown theorem by means of displacement finite element method and nonlinear programming, the shakedown limit of strip footing on cohesive slopes under simultaneous horizontal and vertical repeated loads is investigated. The results are presented in the form of dimensionless charts. The effect of the cohesion and unit weight of the soil, the distance of the footing from the crest of the slope, and the angle of the slope, on the shakedown failure envelope, is studied.

Stability analysis of a cave excavated in granular cohesionless material

The paper presents an analysis of the long-term stability of a large unsupported cave excavated in granular cohesionless material in Ficulle, Italy. The stability of the cave arises from a ‘cohesive’ term in the shear strength criterion and this paper investigates the source of this cohesive term. Contrary to expectations, the material appeared to be granular (cohesionless) at the touch. The investigation started by determining whether the stability of the cave was attributable to any cementation bonding the soil particles. Microstructural analyses, together with geomechanical testing, produced enough evidence to suggest that the material was not naturally cemented. On the other hand, water-undrained direct shear tests on unsaturated intact specimens indicated the presence of significant apparent cohesion, which was then linked to the existence of suction in the material. In this way, the stability of the cave was assessed accounting for the beneficial effects of suction and partial saturation on shear strength. A three-dimensional analysis based on the upper bound theorem of plasticity was successful in confirming the stability of the cave in terms of the state of the structure at the time of field investigation. In addition, it was shown that 24 and 48 h rainfalls of 100 years return period are not sufficient to relieve suction sufficiently to bring the cave to collapse, thus justifying the observed long-term stability of the cave. Suction is rarely included in geotechnical design under the assumption that it cannot be relied upon owing to the potentially adverse effect of rainwater infiltration. This case study demonstrates that suction can indeed remain ‘active’ naturally for a long time, contributing to the long-term stability of geo-structures.

The upper bound theorem for flag homology 5-manifolds

We prove that among all flag homology 5-manifolds with n vertices, the join of 3 circles of as equal length as possible is the unique maximizer of all the face numbers. The same upper bounds on the face numbers hold for 5-dimensional flag Eulerian normal pseudomanifolds.

Almost simplicial polytopes: the lower and upper bound theorems

this is an extended abstract of the full version. We study n-vertex d-dimensional polytopes with at most one nonsimplex facet with, say, d + s vertices, called almost simplicial polytopes. We provide tight lower and upper bounds for the face numbers of these polytopes as functions of d, n and s, thus generalizing the classical Lower Bound Theorem by Barnette and Upper Bound Theorem by McMullen, which treat the case s = 0. We characterize the minimizers and provide examples of maximizers, for any d.

The flag upper bound theorem for 3- and 5-manifolds

We prove that among all flag 3-manifolds on n vertices, the join of two circles with [n 2] and [n 2] vertices respectively is the unique maximizer of the face numbers. This solves the first case of a conjecture due to Lutz and Nevo. Further, we establish a sharp upper bound on the number of edges of flag 5-manifolds and characterize the cases of equality. We also show that the inequality part of the flag upper bound conjecture continues to hold for all flag 3-dimensional Eulerian complexes and characterize the cases of equality in this class.

3D homogenized limit analysis of non-periodic multi-leaf masonry walls

This paper presents a 3D model aiming at investigating the out-of-plane collapse behavior of multi-leaf non-periodic masonry walls. These structural elements are widely employed in several constructions that are part of the European architectural heritage, but have been seldom addressed in the available literature due to their natural complexity and uniqueness. Specifically, the model here proposed allows a quick assessment of the out-of-plane collapse behavior of multi-leaf walls through the extraction of out-of-plane homogenized failure surfaces, acting as macroscopic failure criteria in bending and torsion. These failure surfaces are obtained after solving a standard-form linear programming problem written into a MATLAB script, which expresses a limit analysis problem pairing the well-established upper bound theorem and a homogenization approach. A twofold numerical application is performed by investigating a rubble masonry three-leaf wall and a quasi-regular three-leaf wall; in the latter case study, the influence of the rate of transversal interconnection between the outer wythes of the wall is also investigated. The results show that the presence of two different masonry bonds in the outer wythes entails some changes in the out-of-plane collapse behavior of the two case studies: namely, the out-of-plane response of the wall both under flexural and torsional actions is increased for the rubble masonry three-leaf wall, whereas it is decreased for the quasi-regular three-leaf wall. Moreover, in the latter case it is once more confirmed that a good transversal interconnection between the outer wythes - usually brought by the presence of transversal bricks – has beneficial effects on its out-of-plane collapse behavior, which are displayed both by the out-of-plane homogenized failure surfaces and deformed shapes at collapse.

Finite-element upper-bound analysis of seismic slope stability considering pseudo-dynamic approach

The present study presents a novel procedure to assess the seismic slope stability, using the finite-element upper-bound method combined with the pseudo-dynamic approach. A pioneering work is performed to incorporate the pseudo-dynamic accelerations into the finite-element upper-bound analysis which combines the advantages of upper bound and finite element methods. The finite element method is principally used to discretize the domain of soil mass into finite elements, aiming to construct a kinematically admissible failure mechanism based on which the external and internal rates of work can be expressed. Based on the upper bound theorem, the upper bound formulations are derived from the virtual work rate equation, in the form of slope safety factor and limit surcharge acting on the slope crest. The problem of seeking the optimal upper bound solution is transformed to solve a linear programming problem within numerous kinematically admissible velocity fields, and this is achieved by using the interior-point algorithm implemented into the MATLAB. Pseudo-dynamic solutions are calculated and compared with the pseudo-static, limit equilibrium and FLAC results. The proposed procedure is versatile in considering the homogeneity and non-homogeneity of soil strength properties in seismic slope stability analysis. A benchmark problem with 0.5 m thick weak interlayer is discussed.

Influence of Anisotropy and Nonhomogeneity on Stability Analysis of Fissured Slopes Subjected to Seismic Action

Based on the upper bound theorem of limit analysis, this paper presents a procedure for assessment of the influence of the soil anisotropy and nonhomogeneity on the stability of fissured slopes subjected to seismic action. By means of a mathematical optimization procedure written in Matlab software codes, the stability factorsNSandλcφare derived with respect to the best upper bound solutions. A series of stability charts are obtained in this paper, and then the critical locations of cracks are determined for cracks of known depth. The results demonstrate a significant influence of the soil anisotropy and nonhomogeneity on the stability of the fissured slopes and the location distribution of the cracks. In addition, the procedures for getting the factor of safety are put forward. It is shown that a decrease in the nonhomogeneity coefficientn0and an increase in the anisotropy coefficientkcould lead to the fissured slopes becoming unsafe. Finally, this article also illustrates the variation in the safety factor of fissured slopes under the impact of three factors (Kh,H1/H, andλ).

Three-Dimensional Collapse Analysis for a Shallow Cavity in Layered Strata Based on Upper Bound Theorem

Layered rock strata are observed to be common during the excavation of tunnels or cavities, and may significantly affect the deformation and failure characteristics of surrounding rock masses due to various complex forms an... | Find, read and cite all the research you need on Tech Science Press

Prediction of the Collapse Region Induced by a Concealed Karst Cave above a Deep Highway Tunnel

The presence of a concealed karst cave above a deep highway tunnel may cause the collapse of the rock mass between the karst cave and tunnel during excavation. Rock mass collapse threatens the safety of tunnel construction personnel. A prediction method of the collapse region induced by a concealed karst cave above a deep highway tunnel is proposed on the basis of the upper bound theorem of limit analysis. An analytical expression of the collapse surface is derived from the variational principle. Using the analytical expression of the collapse surface, the shapes of the collapse surfaces are plotted for different rock mass parameters. Moreover, the minimum safe distance between the karst cave and tunnel is defined, and the computational equation of the minimum safe distance is derived. The proposed method is applied in a highway tunnel excavated in a karst terrain as a case study. Based on geological survey report parameters, the shape of the collapse surface and the minimum safe distance between the karst cave and tunnel are obtained. Finally, the collapse surface of the rock mass provided by the proposed approach is compared with that provided by numerical simulation, and the favorable result comparison shows that the proposed method is valid.