Search

The discovery of frequent closed high utility itemsets (FCHUIs) and frequent generators of high utility itemsets (FGHUIs) is significant because they serve as important and concise representations of frequent high utility itemsets (FHUIs), offering a brief but essential summary that can be considerably smaller. Besides, they facilitate the generation of nonredundant high utility association rules that are crucial for decision-makers. However, the challenge lies in the difficulty of mining these representations due to scalability issues, high memory usage, and long runtimes, particularly when dealing with dense and large datasets. To address this issue, this paper proposes a novel approach for efficiently mining FCHUIs and FGHUIs using a novel weak lower bound named w l b u on the utility. The approach includes effective pruning strategies for early eliminating non-closed and/or non-generator high utility branches in the prefix search tree based on w l b u. These pruning strategies allow faster execution with lower memory usage. In addition, the paper presents two novel algorithms, FCGHUI-Miner and FGHUI-Miner, which can simultaneously discover both FGHUIs and FCHUIs or solely mine FGHUIs, respectively. The experimental results demonstrate that the proposed algorithms outperform state-of-the-art algorithms in terms of efficiency and effectiveness. [ABSTRACT FROM AUTHOR]

The partially randomized extended Kaczmarz method is effective for solving large, sparse, overdetermined and inconsistent linear systems. In this paper, we propose a modified variant for this method, and give a tight upper bound for its convergence rate. Moreover, we verify the efficiency of the proposed method by numerical experiments. [ABSTRACT FROM AUTHOR]

Robotic Process Automation (RPA) is used in various fields of human activity in order to implement faster and more secure processes through a reduction in the risks or errors but also an increase in the productivity rates. The increase of its use and importance calls for evermore efficient solution methods for this problem. In this paper, the RPA is addressed in the context of a financial institution. The problem consists in assigning transactions to software robots, where each transaction type has a different clearance date and a different processing time. First, four heuristics are used to compute an upper bound on the number of required software robots. Then, this bound is given as a parameter to an integer linear program, which is used to assign the transactions to the different robots. The quality of the solutions is assessed by an extensive experimental study on a set of 39,000 instances. The results show that two heuristics outperform the others and allow for a faster resolution by the integer linear program which in turn finds the optimal solution for most of the instances within a timeout of 60 seconds. [ABSTRACT FROM AUTHOR]

The locating-chromatic number of a graph G (V , E) is the cardinality of a minimum resolving partition of the vertex set V (G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices not contained in the same partition class. Determining the locating-chromatic number of any tree is a difficult task. In this paper, we propose an algorithm to compute the upper bound on the locating-chromatic number of any tree. To do so, we decompose a tree into caterpillars and then compute the upper bound of the locating-chromatic number of this tree in terms of the ones for these caterpillars. [ABSTRACT FROM AUTHOR]

Let G be a graph on n vertices and λ 1 , λ 2 , ... , λ n their eigenvalues. The Estrada index of G is defined as E E (G) = ∑ i = 1 n e λ i . In this paper, we obtain new upper and lower bounds on the Estrada Index of a given graph, considering numerical inequalities present in the literature. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph with n vertices and m edges. The spectral radius ρ (G) of G is the largest eigenvalue of its adjacency matrix. In this paper, we firstly consider the effect on the spectral radius of a graph by removing a vertex, and then as an application of the result, we obtain a new sharp upper bound of ρ (G) which improves some known bounds: If (k − 2) (k − 3) 2 ≤ m − n ≤ k (k − 3) 2 , where k (3 ≤ k ≤ n) is an integer, then ρ (G) ≤ 2 m − n − k + 5 2 + 2 m − 2 n + 9 4 . The equality holds if and only if G is a complete graph K n or K 4 − e , where K 4 − e is the graph obtained from K 4 by deleting some edge e. [ABSTRACT FROM AUTHOR]

The size of a largest independent set of vertices in a given graph G is denoted by α (G) and is called its independence number (or stability number). Given a graph G and an integer K , it is NP-complete to decide whether α (G) ≥ K. An upper bound for the independence number α (G) of a given graph G with n vertices and m edges is given by α (G) ≤ p ≔ ⌊ 1 2 + 1 4 + n 2 − n − 2 m ⌋. In this paper we will consider maximum independent sets near this upper bound. Our main result is the following: There exists an algorithm with time complexity O (n 2) that, given as an input a graph G with n vertices, m edges, p ≔ ⌊ 1 2 + 1 4 + n 2 − n − 2 m ⌋ , and an integer k ≥ 0 with p ≥ 2 k + 1 , returns an induced subgraph G p , k of G with n 0 ≤ p + 2 k + 1 vertices such that α (G) ≤ p − k if and only if α (G p , k) ≤ p − k. Furthermore, we will show that we can decide in time O (1. 273 8 3 k + n 2) whether α (G p , k) ≤ p − k. [ABSTRACT FROM AUTHOR]

Let G = (V (G) , E (G)) be a weighted digraph with vertex set V (G) = { v 1 , v 2 , ... , v n } and arc set E (G) , where the arc weights are nonzero nonnegative symmetric matrices. In this paper, we obtain an upper bound on the signless Laplacian spectral radius of a weighted digraph G , and if G is strongly connected, we also characterize the digraphs achieving the upper bound. Moreover, we show that an upper bound of weighted digraphs or unweighted digraphs can be deduced from our upper bound. [ABSTRACT FROM AUTHOR]

Abstract Let G = (V , E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S , and every vertex in V − S is adjacent to a vertex in V − S. The total restrained domination number of G , denoted γ t r (G) , is the smallest cardinality of a total restrained dominating set of G. In Koh et al. (2013), it is proved that if G is a graph of order n ≥ 4 and δ (G) ≥ 2 , then γ t r (G) ≤ n − n 4 3. It is further conjectured that this bound can be improved to γ t r (G) ≤ n − θ (n). In this paper we show that if G is a graph with no C 3 components and δ (G) ≥ 2 , then γ t r (G) ≤ n − n 2 . [ABSTRACT FROM AUTHOR]

Highlights • The consistency principle is proposed to estimate the model parameter on image noise removal problem. • A dual method is developed simultaneously to solve the optimization problem and to find the regularization parameter. • The gain can be as great as 2.23 dB in PSNR by the proposed method. Abstract Total variation regularized model is a powerful tool in image noise removal due to its edge-preserving property of an image. One important procedure in the model is to determine the regularization parameter which has an important role in balancing the data-fidelity and the regularity of the denoised image. Discrepancy principle is a classical method for selecting the regularization parameter, which provides an upper bound for the value of the data-fitting term. For the regularization parameter, it is easier to estimate its upper bound as the statistical property of the noise is known. The contribution of this paper is twofold. First, we propose an iterative algorithm to estimate an optimal upper bound by applying the consistency between the value of data-fitting term and the upper bound. Second, we develop a dual-based method to solve the constrained problem which can avoid the computation of the Lagrangian multiplier associated with the constraint. The new algorithm can simultaneously solve the solution of the constrained problem and the estimate of the regularization parameter. Numerical results are given to show that the proposed algorithm is better than some state-of-the-art methods in both efficiency and accuracy. [ABSTRACT FROM AUTHOR]

Abstract An edge metric generator of a connected graph G is a vertex subset S for which every two distinct edges of G have distinct distance to some vertex of S , where the distance between a vertex v and an edge e is defined as the minimum of distances between v and the two endpoints of e in G. The smallest cardinality of an edge metric generator of G is the edge metric dimension, denoted by dim e (G). It follows that 1 ≤ dim e (G) ≤ n − 1 for any n -vertex graph G. A graph whose edge metric dimension achieves the upper bound is topful. In this paper, the structure of topful graphs is characterized, and many necessary and sufficient conditions for a graph to be topful are obtained. Using these results we design an O (n 3) time algorithm which determines whether a graph of order n is topful or not. Moreover, we describe and address an interesting class of topful graphs whose super graphs obtained by adding one edge are not topful. [ABSTRACT FROM AUTHOR]

Previous cavity expansion analyses are all performed in infinite soil. However, cavity expansion problem in half space (or semi-infinite soil) is also required in geotechnical engineering (tunneling and compaction grouting). New upper and lower bound solutions are derived for expanded spherical and cylindrical cavities in half space of Tresca soil based on the method of finite element limit analysis in this paper. Two types of case, namely homogenous soil and non-homogenous soil with undrained strength linearly increased with depth, are consider in the analysis. Simple empirical closed-form equations are then proposed for predicting the limit cavity expansion pressure through nonlinear regression analysis. The present solutions provide theoretical reference for the corresponding geotechnical engineering problems such as tunneling and compaction grouting. [ABSTRACT FROM AUTHOR]

This paper has been prepared in memory of Professor Scott Sloan. It first presents a brief review of the development of shakedown analysis methods for pavement and railway engineering problems. In particular, it describes a new lower-bound method using the concept of critical residual stress fields and an upper-bound method using a nonlinear programming technique, which were developed by the authors, and then extended and applied to solve various shakedown problems in pavement and railway engineering. Moreover, this paper summarises and compares shakedown solutions for pavement and railway engineering problems, whilst highlighting the key factors that influence the shakedown limits. In addition, this paper proposes a simple, unified shakedown limit equation for pavements and railways under repeated moving surface loads. The equation includes three terms, which represent the resistances from cohesion, self-weight of the underlying soil, and self-weight of any superficial rigid layers, respectively, in a format analogous to Terzaghi's bearing capacity equation. Numerical results indicate that the coefficient in the cohesion term N c sd depends on the soil friction angle; while the coefficient in the self-weight term N γ sd is controlled by the soil friction angle and a dimensional factor γ a / c. Values of N c sd and N γ sd for a typical rolling point contact problem are also presented and interpreted, which explain the different contribution ratios from the soil self-weight to the shakedown limits of pavement and railway problems. [ABSTRACT FROM AUTHOR]

Mining high-utility patterns in databases containing items with both positive and negative profits is useful in market basket databases, since negative profits are common in the real world. Obviously, in the market basket database, patterns with stable long-term profits have more meaning. The discovery of itemsets with a consistent high frequency is known as periodic frequent pattern mining. Therefore, mining periodic high-utility patterns in a database containing items with both positive and negative profits is an interesting and useful task. However, this task has two main challenges. First, the utility measure does not have the download closure property. Second, the huge search space needs to be pruned more effectively. In this paper, we propose a vertical data structure-based algorithm called PHMN to discover periodic high-utility patterns (PHUPs) or itemsets in a transaction database with both positive and negative utilities. To be more efficient, we propose a new upper bound to prune the search space and an improved algorithm to discover the PHUPs. Finally, experiments are conducted to verify the effectiveness and efficiency of algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of an m -order n -dimensional generalized Hilbert tensor H n = ( H i 1 i 2 ⋯ i m ) , H i 1 i 2 ⋯ i m = 1 i 1 + i 2 + ⋯ i m − m + a , a ∈ R ∖ Z − ; i 1 , i 2 , ⋯ , i m = 1 , 2 , ⋯ , n , and show that its H -spectral radius and its Z -spectral radius are smaller than or equal to M ( a ) n m − 1 and M ( a ) n m 2 , respectively, here M ( a ) is a constant depending on a . Moreover, both infinite and finite dimensional generalized Hilbert tensors are positive definite for a ≥ 1 . For an m -order infinite dimensional generalized Hilbert tensor H ∞ with a > 0 , we prove that H ∞ defines a bounded and positively ( m − 1 ) -homogeneous operator from l 1 into l p ( 1 < p < ∞ ) . Two upper bounds on the norms of corresponding positively homogeneous operators are obtained. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamic analysis of Bernoulli-Euler beams with uncertain parameters crossed by moving loads. Uncertainties associated with mass density, Young’s modulus and load velocity are modeled as interval variables with given lower bounds and upper bounds. In order to evaluate the bounds of the interval displacement of the beam, an efficient procedure based on the use of the classical modal superposition method in conjunction with the improved interval analysis via extra unitary interval is developed. The key idea is to seek the bounds of the response by exploring just a few combinations of the endpoints of the uncertain parameters appropriately selected based on those yielding the minimum and maximum values of the interval natural frequencies. [ABSTRACT FROM AUTHOR]

Currently, geosynthetic reinforcements are calculated assuming the backfill to be purely frictional. However, accounting for the presence of even a modest amount of cohesion may allow using locally available cohesive backfills to a greater extent and less overall reinforcement. Unlike purely frictional backfills, cohesive soils present are subject to the formation of cracks that tend to reduce slope stability which therefore need to be properly accounted for in any slope stability assessment. Utili & Abd [1] derived a semi-analytical method for uniform c- ϕ slopes accounting for the presence of cracks that provides the amount of reinforcement needed as a function of soil cohesion, tensile strength, angle of shearing resistance and slope inclination employing the limit analysis upper bound method. In this paper the formulation is extended to the seismic case, accounting for earthquake action by employing the pseudo-static approach. Ready to use design charts providing the value of the required reinforcement are plotted for both uniform and linearly increasing reinforcement distributions. From the results it emerges that accounting for the presence of cohesion allows significant savings to be made, but the presence of seismic action may require considerable additional reinforcement. [ABSTRACT FROM AUTHOR]

Weighted Frequent Itemset Mining (WFIM) has been proposed as an extension of frequent itemset mining that considers not only the frequency of items but also their relative importance. However, using WFIM algorithms in real applications raises some problems. First, they do not consider how recent the patterns are. Second, traditional WFIM algorithms cannot handle uncertain data, although this type of data is common in real-life. To address these limitations, this paper introduces the concept of Recent High Expected Weighted Itemset (RHEWI), which considers the recency, weight and uncertainty of patterns. By considering these three factors, more up-to-date and relevant results are found. A projection-based algorithm named RHEWI-P is presented to mine RHEWIs using a novel upper - bound downward closure ( UBDC ) property. An improved version of this algorithm called RHEWI-PS is further proposed based on a novel sorted upper-bound downward closure ( SUBDC ) property for pruning unpromising candidate itemsets early. An experimental evaluation against the state-of-the-art HEWI-Uapriori algorithm was carried out on both real-world and synthetic datasets. Results show that the proposed algorithms are highly efficient and are acceptable for mining the desired patterns. [ABSTRACT FROM AUTHOR]

Let B ( n , k ) be the set of all ( 0 , 1 ) -matrices of order n with constant line sum k and let ν ˜ ( n , k ) be the minimum rank over B ( n , k ) . It is known that ⌈ n / k ⌉ ≤ ν ˜ ( n , k ) ≤ ν ˆ ( n , k ) ≤ ⌊ n / k ⌋ + k , where ν ˆ ( n , k ) is the rank of a recursively defined matrix A ˆ ∈ B ( n , k ) . Brualdi, Manber and Ross showed that ν ˜ ( n , k ) = ⌈ n / k ⌉ if and only if k | n . In this paper, we show that ν ˜ ( n , k ) = ⌊ n / k ⌋ + k if and only if ( n , k ) satisfies one of the following three relations: (i) n ≡ ± 1 ( mod k ) , k = 2 or 3; (ii) n = k + 1 , k ≥ 2 ; (iii) n = 4 q + 3 , k = 4 and q ≥ 1 . Moreover, we obtain the exact values of ν ˜ ( n , 4 ) for all n ≥ 4 and determine all the possible ranks of regular ( 0 , 1 ) -matrices in B ( n , 4 ) . We also present some positive integer pairs ( n , k ) such that ν ˜ ( n , k ) < ν ˆ ( n , k ) < ⌊ n / k ⌋ + k , which gives a positive answer to a question posed by Pullman and Stanford. [ABSTRACT FROM AUTHOR]

The Laplacian spread of a graph G with n vertices is defined to be s L ( G ) = μ 1 ( G ) − μ n − 1 ( G ) , where μ 1 ( G ) , μ n − 1 ( G ) are the largest and the second smallest Laplacian eigenvalues of G , respectively. It is conjectured that s L ( G ) ≤ n − 1 . In this paper, we first establish a new sharp upper bound for s L ( G ) , and then use it to prove that the conjecture is true for t -quasi-regular graphs when t ≤ n − 3 + 2 / n . We also present some other partial solutions for this conjecture; in particular, we show that the conjecture holds for K 3 -free graphs. Finally, we give several sharp lower bounds for s L ( G ) as well. [ABSTRACT FROM AUTHOR]

Membrane separation properties are constrained by a tradeoff relationship between permeability and selectivity. This tradeoff relationship has been well established for gas separation membranes in the form of the Robeson's upper bound. In contrast, the upper bound relationship is much less established for thin-film composite (TFC) polyamide membranes used for desalination. In this work, we analyzed the tradeoff between the water permeance and the water/NaCl selectivity for TFC membranes gathered from more than 300 published papers. A clear upper bound behavior relationship is established, and the various effects of membrane synthesis conditions and modifications are reviewed in relation to this permeance-selectivity tradeoff. Our work provides a critical tool for the evaluation and benchmarking of future membrane development works in the context of desalination and water reuse. Image 1 • TFC polyamide membranes are constrained by permeance-selectivity tradeoff. • An upper bound is established based on TFC membranes from >300 papers. • The upper bound is given by A/B = 16000 A −3.2 (A/B in bar−1 and A in Lm−2h−1bar−1). • The effects of various parameters on membrane performance are summarized. [ABSTRACT FROM AUTHOR]

In this paper, the seismic bearing capacity of a strip footing sitting on rock masses has been investigated following the upper bound theorem of limit analysis. The generalized tangential technique is used to obtain the equivalent Mohr–Coulomb parameters of the modified Hoek–Brown criterion. Considering the damping characteristics of the site as well as the dynamic characteristics of the seismic waves, the modified pseudo-dynamic (MPD) method is applied to evaluate the seismic effects. A parametric study is conducted, which shows that the seismic acceleration coefficient, the geological strength index, the material constant of the intact rock, and the normalized frequency all have a significant effect on the seismic bearing capacity. The MPD results are also compared with other methods, including the conventional pseudo-dynamic (CPD) method, spectral pseudo-dynamic method (SPD), and pseudo-static (PS) method. A high degree of agreement can be observed between the MPD results and the CPD results as the normalized frequency increases. When the normalized frequency equals 0.5 + n π , the values of the bearing capacity factor obtained by using the MPD method and the SPD method will hit their local minima, while the CPD and PS methods will overestimate the bearing capacity factor to a large extent. [ABSTRACT FROM AUTHOR]

In this paper, we will estimate the lower and upper bounds of the first eigenvalues for bi-Laplace operators on Finsler manifolds. [ABSTRACT FROM AUTHOR]

This paper presents a kinematic approach of limit analysis to evaluate the effects of nonlinear failure criterion on the three-dimensional (3D) stability analysis of uniform slopes. For slopes in various clays, the upper bounds on the critical heights associated with the linear and nonlinear failure criteria are obtained and comparisons of the linear and nonlinear results are made to investigate their differences. The differences between the linear and nonlinear solutions change with varying slope inclination, resulting in two critical values on the slope inclination angle. In the intermediate range of slope inclinations, the critical heights associated with the linear failure criterion are smaller than the nonlinear results, and the underestimation by using the linear failure criterion cannot be neglected. For other cases, the analyses based on the linear failure criterion will overestimate the stability of actual slopes obeying the nonlinear failure criterion. Meanwhile, the 3D effects have insignificant influences on the two critical slope inclination angles. However, the sensitivity of the critical heights to the nonlinearity of soil strength envelope appears to be more pronounced for slopes with a smaller width. [ABSTRACT FROM AUTHOR]

The packing chromatic number χ ρ ( G ) of a graph G is the smallest integer k needed to proper color the vertices of G in such a way that the distance in G between any two vertices having color i be at least i + 1 . Goddard et al. (2008) found an upper bound for the packing chromatic number of hypercubes Q n . Moreover, they compute χ ρ ( Q n ) for n ≤ 5 leaving as an open problem the remaining cases. In this paper, we obtain a better upper bound for χ ρ ( Q n ) and we improve the lower bounds for χ ρ ( Q n ) for 6 ≤ n ≤ 11 . In particular we compute the exact value of χ ρ ( Q n ) for 6 ≤ n ≤ 8 . [ABSTRACT FROM AUTHOR]

The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion. The cell-based smoothed discrete shear gap method (CS-DSG3) is combined with a second-order cone optimization programming (SOCP) for determining the upper bound limit load of the Mindlin plates. The limit analysis problem of Mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work. This minimization problem is then transformed into an explicit form suitable for the solution using the SOCP. The numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for the Mindlin plates. [ABSTRACT FROM AUTHOR]

Fuzzy utility mining has been an emerging research issue because of its simplicity and comprehensibility. Different from traditional fuzzy data mining, fuzzy utility mining considers not only quantities of items in transactions but also their profits for deriving high fuzzy utility itemsets. In this paper, we introduce a new fuzzy utility measure with the fuzzy minimum operator to evaluate the fuzzy utilities of itemsets. Besides, an effective fuzzy utility upper-bound model based on the proposed measure is designed to provide the downward-closure property in fuzzy sets, thus reducing the search space of finding high fuzzy utility itemsets. A two-phase fuzzy utility mining algorithm, named TPFU , is also proposed and described for solving the problem of fuzzy utility mining. At last, the experimental results on both synthetic and real datasets show that the proposed algorithm has good performance. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the backward error for the symmetric generalized inverse eigenvalue problem, which extends the result of Sun (1999) [10] . The optimal backward error is defined for symmetric generalized inverse eigenvalue problem with respect to an approximate solution, and the upper and lower bounds are derived for the optimal backward error. The expressions may be useful for testing the stability of practical algorithms. [ABSTRACT FROM AUTHOR]

• A state of art approach to study limiting pressure behind soil gaps in contiguous pile walls. • Advanced 2D finite element limit analysis for contiguous pile walls. • Comprehensive design charts and tables are presented. • A closed-form equation of the limiting pressure factor is presented. New average FELA solutions for the problem of the limiting pressure behind soil gaps and the lateral force acting on a pile per unit length of a contiguous pile wall in anisotropic clay are investigated in this paper. The anisotropic undrained shear (AUS) model is utilized to determine anisotropic soil behaviour. The limiting pressure factor (N) is derived by varying dimensionless parameters such as the anisotropic ratio (r e), the adhesion factor (α), and soil gap ratios (S/D) which are presented in the form of sample charts and tables. The failure patterns of the soil gaps are also conducted and explained in light of the impacting factors. A closed-form equation of the limiting pressure factor is presented in order to efficiently and precisely establish and evaluate an undrained limiting pressure behind soil gaps and the lateral force operating on a pile wall in practice. [ABSTRACT FROM AUTHOR]

In this paper, we address the exact solution of the vertex bisection problem (VBP). We propose two novel B&B algorithms to solve VBP, which include new upper and lower bound constructive heuristics, and an efficient strategy to explore the combinatorial search space. The computational results show that the proposed algorithms clearly outperforms the state-of-the-art B&B algorithm in quality and efficiency. The two proposed B&B versions differ in the exploration strategy and the storage of the search tree. Also, we provide four new solutions, previously unknown. We consider that the main contributions of this work can be adapted to solve combinatorial problems in other related domains. • Two representations of the search tree for the branch and bound algorithm. • Two new greedy constructive heuristics for the vertex bisection problem. • A new lower bound computation for the vertex bisection problem. • New optimal solutions for four Harwell–Boing instances. [ABSTRACT FROM AUTHOR]

In geological engineering, the unsaturation and non-uniformity of soil have significant influence on slope stability. However, they were common neglected in published literature. Based on the three-dimensional (3D) rotational failure mechanism, this paper introduces a method that combines the gravity increase method and the upper bound theorem, to evaluate the factor of safety (FS) of 3D stepped slope in non-uniform and unsaturated soils. The soil cohesion increases linearly with depth, and three nonlinear unsaturated shear strength models are adopted in this study. After the calculations of internal energy dissipation rate and external work rate, the analytical formula of FS is derived, and the lowest FS value is obtained through optimization. To prove the validity of the proposed method, the present results are compared with previously published solutions. A parametric study is carried out, and the influences of a number of factors on FS are discussed. For non-uniform and unsaturated soils, the new formula for calculating the FS of 3D two-stage slopes is presented for practical use in geological engineering. • New formula for calculating the FS of 3D two-stage slopes is derived. • GIM is introduced to evaluate FS of 3D stepped slopes in inhomogeneous and unsaturated soils. • Validity of the analytical solutions obtained in this study is verified. [ABSTRACT FROM AUTHOR]

This paper explores a pathway for increasing efficiency in numerical 3D limit analysis through r - h adaptivity, wherein nodal positions (r) and element lengths (h) are successively refined. The approach uses an iterative, nested optimization procedure involving three components: (1) determination of velocities for a fixed mesh of rigid, translational elements (blocks) using second-order cone programming; (2) adaptation of nodal positions using non-linear optimization (r adaptivity); and (3) subdivision of elements based on the magnitude of the velocity jumps (h adaptivity). Examples show that the method can compute reasonably accurate limit loads at relatively low computational cost. [ABSTRACT FROM AUTHOR]

This paper investigates the three-dimensional (3D) stability of a circular tunnel in drained cohesive-frictional soil. Numerical simulations are performed to study the face stability of a circular tunnel for various soil properties and tunnel diameter-to-depth ratios. The finite element limit analysis (FELA) is employed to determine rigorous upper and lower bounds solutions of tunnel stability factors (F c , F s and F γ), which are functions of the depth ratio and soil internal friction angle. These stability factors are used to estimate the critical heading pressures at collapse. The obtained results are compared with existing published solutions in the literature. The study aims to improve the available solutions by using the latest 3D finite element limit analysis technique. A number of examples are provided, which demonstrate the practical use of the three stability factors in estimating tunnel heading pressures. [ABSTRACT FROM AUTHOR]