Upper-bound Solution Research Articles

Cohesive-strength properties versus porosity of cementitious materials

This paper presents a new approach for quantifying the effect of porosity, at meso and macro-scales, on the strength behaviour of cementitious materials at a macro-scale. The proposed approach combines a cohesive-strength homogenisation model with second-order cone programming through establishing the analytical upper bound solution of cohesive-strength behaviour using inverse analysis. The derived formulation presents a nonlinear relationship between the uniaxial compressive strength-to-porosity ratio and the material parameters of the developed homogenisation model. The results show that the curing ages increase the friction coefficient, cohesion and the mesoporosity of the hydration products, while the macroporosity decreases. The results also show that the volume fraction of the solid hydration products decreases with curing ages but the increase in the mesoporosity causes the expansion of the porous hydration products at mesoscales This outcome provides a compelling new evidence that the development of the hydration products of cementitious materials affects the volume fraction of pores in which meso and macroporosity are inversely related.

Generalized Degrees of Freedom of Noncoherent Diamond Networks

We study the generalized degrees of freedom (gDoF) of the noncoherent diamond (parallel relay) wireless network with asymmetric distributions of link strengths. We use the noncoherent block-fading model introduced by Marzetta and Hochwald, where no channel state information is available at the transmitters or at the receivers and the channels remain constant for a coherence time of $T$ symbol durations. We first derive an upper bound for the capacity of this channel and then derive the optimal structure for the solution of the upper bound optimization problem. Using the optimal structure, we solve the upper bound optimization problem in terms of its gDoF. Using insights from our upper bound signaling solution, we devise an achievability strategy based on a novel scheme that we call train-scale quantize-map-forward (TS-QMF). This scheme uses training in the links from the source to the relays, scaling and quantizing at the relays combined with nontraining-based schemes. We show the optimality of this scheme by comparing it to the upper bound in terms of the gDoF. In noncoherent point-to-point multiple-input-multiple-output (MIMO) channels, where the fading realization is unknown to the transmitter and the receiver, an important tradeoff between communication and channel learning was revealed by Zheng and Tse, by demonstrating that not all the available antennas might be used, as it is suboptimal to learn all their channel parameters. Our results in this paper for the diamond network demonstrate that in certain regimes of relative channel strengths, the gDoF-optimal scheme uses a subnetwork, demonstrating a similar tradeoff between channel learning and communication. In some regimes, it is gDoF-optimal to do relay selection, i.e., use a part of the network. In the other regimes, even when it is essential to use the entire network, it is suboptimal to learn the channel states for all the links in the network, i.e., traditional training-based schemes are suboptimal in these regimes.

An upper bound solution for tunnel face stability analysis considering the free span

One of the main factors that affect the tunnel face stability is the free or unsupported span (i.e., the unlined length adjacent to the tunnel face). In this work, a 2D failure mechanism is developed to compute, in the context of Limit Analysis, the collapse pressure for tunnel faces in Mohr-Coulomb materials, considering the free span. The new mechanism comprises three non-deformable blocks (two translational and one rotational) in such a way that the interface between one of the translational blocks and the rotational one is constructed by an iterative process that fulfills the associated flow rule imposed by Limit Analysis. A numerical model is employed to validate the proposed mechanism, demonstrating that it provides good predictions of the critical pressure and of the failure geometry, especially for tunnels in materials with higher friction angles (i.e., φ≥35°). Results confirm the expected increase of the collapse pressure with the free span; however, the increase is noticeably higher when no pressure is applied on the free span than when the support pressure is applied on the tunnel face and on the free span, especially for cases with lower cohesion (i.e., c≤15kPa). In addition, the effect of a forepole umbrella is incorporated into the Limit Analysis mechanism, and a new methodology is proposed to estimate the collapse pressure when a forepole umbrella is installed at the face. Results of the analytical solution in this situation are compared with those of the numerical model, with results confirming that the proposed mechanism is able to capture the stability improvement (i.e., the reduction of the collapse pressure) produced by the umbrella, as well as the shape changes of the failure mechanism; in particular, it can predict a local failure of the face below heavy umbrellas.

Seismic Bearing Capacity of Strip Footings on Ground Reinforced by Stone Columns Using Upper-Bound Solutions

Abstract In this technical note, the seismic bearing capacity coefficients of shallow foundations placed on soft ground reinforced by stone columns are evaluated based on the upper-bound theorem of...

Three-dimensional upper bound limit analysis of underground cavities using nonlinear Baker failure criterion

A generalized nonlinear Baker failure criterion is employed with the upper bound limit analysis to study the surrounding rock stability of underground cavities. A three-dimensional (3D) failure mode is established by extending the two-dimensional (2D) failure mode, which offers an upper bound expression of the surrounding rock pressure. This method is validated with a series of examples before the influence of four parameters of scale parameter, curvature parameter, shift parameter and lateral pressure coefficient, on the surrounding rock pressure is analyzed. According to these results, failure ranges of the underground cavities are determined. The following conclusions are reached: (1) the proposed approach is more accurate to predict surrounding rock pressure than the Mohr−Coulomb failure criterion; (2) the surrounding rock with large scale parameter, curvature parameter, shift parameter, and lateral pressure coefficient can lead to a more stable underground cavity; (3) the failure range in 3D mode can be predicted according to the upper bound solutions.

Fault-Tolerant Control for Stochastic Switched IT2 Fuzzy Uncertain Time-Delayed Nonlinear Systems.

This article devotes to solve the fault-tolerant control problem based on interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy stochastic switched uncertain time-delayed systems with signal quantization. Stochastic switched systems can model a dynamic structure susceptible to abrupt faults, making it more practically significant in power systems or economic systems. The core design is an observer-based fault-tolerant control scheme that can estimate incomplete measurable variables and eliminate the influence of fault dynamically well and enhancing the robust stability of the systems subject to quantization effects. A novel method in seeking the upper bound solution of time-varying delay efficiently decreases conservativeness, especially for the proposed time-delayed system. The simulated analysis is specified to verify the availability and validity of the obtained design method.

Undrained capacity of circular foundations under combined horizontal and torsional loads

Torsional loads can be significant on the shallow foundations of large onshore and offshore structures. However, the effect of torsional loads in isolation and in combination with other load directions has not been well studied. In this paper, a failure envelope for combined horizontal (H) and torsional load (T) for circular surface foundations on soils under undrained conditions has been derived using the upper-bound plasticity method. In addition, this solution is compared with finite-element model results and theoretical solutions for the uniaxial capacity for H and T. The H–T failure envelope obtained from a conventional design standard method (i.e. DNVGL-ST-0126) is also compared with the upper-bound solution. The upper-bound solution is in excellent agreement with the finite-element results, and the codified H–T failure envelope appears to be conservative compared with the other methods. This approach can help validate finite-element results and aid the assessment of the ultimate capacity of shallow circular foundations under combined horizontal and torsional loading.

Application of T-EMSD based p-y curves in the three-dimensional analysis of laterally loaded pile in undrained clay

To apply the p-y curve method in laterally loaded pile analyses, three-dimensional effects in component such as the ultimate pile bearing capacity, pile compatibility factor and initial subgrade modulus must be incorporated. A framework to consider these factors in the theoretical p-y curve derived by the Total-displacement-loading Extended Mobilisable Strength Design (T-EMSD) approach is presented. The bearing capacity design equation can be used to estimate the continuous velocity fields based pile compatibility factor profile. To verify the pile bearing capacity design equation fitted from an upper-bound solution, centrifuge experiments of rigidly translated piles were performed. Corresponding finite element analyses were also performed. The pile compatibility factor profile was obtained through the verified bearing capacity equation and experimental results. Finally, the applications of plane-strain p-y curves to three-dimensional problems were demonstrated via experiment simulation and parametric study.

Ultimate bearing capacity of skirted foundation on cohesionless soil using slip line theory

Abstract A plasticity-based model is developed under the framework of the slip line theory to estimate the ultimate bearing capacity of a skirted strip foundation resting on cohesionless soil under both static and seismic conditions. The analysis is performed considering a both-side failure mechanism beneath the foundation. The bearing capacity is eventually derived by satisfying the force equilibrium of the soil wedge trapped between the skirts. A pseudo-static analysis is performed to encompass the effect of an earthquake in the present analysis. The enhancement in the bearing capacity of a skirted foundation compared to a conventional surface foundation is demonstrated with a comprehensive parametric study. The obtained results are found to be lesser than that obtained through the upper bound solution reported in the literature but closer to the available experimental studies. Reduction in the bearing capacity of a skirted foundation during any seismic event is found to be lesser due to the presence of the skirts.

An Upper Bound Solution for Continued Compression of a Cylinder

An Upper Bound Solution for Continued Compression of a Cylinder

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.

Mathematical modeling of closure behavior for a centrally elliptical void in thick slab

To investigate the evolution behavior of a centrally elliptical void in thick slab during rolling, a critical criterion for closing a central elliptical void is established through the energy analysis. According to the condition of volume constancy, a triangular velocity field embedding an elliptical void is established. Based on the velocity field, the minimum value of rolling energy rate, composed of shear energy rate and cracking energy rate, is calculated. According to the balance principle of energy rate, the expression of relative stress factor is obtained. Then, a mechanical criterion for void closure is derived from the basis of extreme condition, and the effects of void size, aspect ratio, geometrical shape parameter, thickness-to-radius ratio, and the relative reduction on the void closure are analyzed. Several rolling processes with different elliptical voids under seven aspect ratios are simulated by the finite element method (FEM), and the evolution characteristic of the void is revealed. The analytical results based on the mechanical criterion and those by the FEM are compared. It is shown that the two prediction results are in good agreement, and a flat void is easier to be closed than a sharp one. Also, the simulated rolling force and torque are obtained through the FEM model, and the comparison result confirms the validity of the upper bound solution. Finally, a rolling experiment with a prefabricated void is carried out to check the reliability of the closure criterion, and a good consistence is also found. In addition, the shortage of the present investigation based on 2D simulation for assessing the mechanical criterion is discussed as a prospect of the future research.

An Applied Analytical Method for the Forward Extrusion of Metals

An applied analytical formulation was developed to deal with the forward extrusion of non-symmetric sections based on the upper bound method. This method of solution has been developed as an alternative to finite element method with the advantages of less time consumption and expense. The deforming region where the material flow occurs was formulated in a new and more realistic fashion by streamlines and stream surfaces. Streamlines and stream surfaces were defined parametrically for the material flow and the development of the kinematically admissible velocity field. The newly developed velocity field incorporated features such that the real physical aspects of the problem were followed more closely than before. The internal, shear and frictional power terms were obtained from the upper bound solution. Using the present method of analysis, the pattern of material flow and the relative extrusion pressure were computed. Results compared to previous works indicated substantial improvements. Experimental and numerical investigations were carried out, and the proposed theoretical model was verified. Close agreement was observed between the analytical results and those from the simulation and the experiment.

Bearing capacity of a strip footing placed next to an existing footing on frictional soil

The ultimate bearing capacity of a single/isolated footing has been investigated intensively by many researchers. Although a lot of studies considered different aspects affecting the bearing capacity, only very few focused on the influence of an existing footing on the bearing capacity of a new footing in its close proximity. In this study, the influence of an existing footing on the ultimate bearing capacity of a recently constructed footing in a close spacing has been investigated with respect to different sizes of the footings, spacings between the footings, friction angles of the subsoil and loads applied on the existing footing. Numerical simulations based on finite-element limit analysis (FELA) are utilized to determine lower and upper bounds of the ultimate bearing capacity which bracket the exact solution from below and above. The results for isolated footings are compared with selected data from literature in terms of the bearing capacity factor Nγ indicating good agreement of both, lower and upper bound values. Accuracy of the results was enhanced by applying an adaptive mesh refinement technique which enabled a more precise approximation of the failure mechanism and a better estimation of the exact solution due to smaller differences between the lower and upper bound solutions. The results for footings placed next to an existing footing are discussed with regard to the interference factor ξγ as well as the shape and size (extend) of the failure mechanism. The results illustrate that two types of failure mechanisms may develop which either extend up to the front edge of the existing footing or pass underneath. Comparisons with previous studies revealed that interference factors have been improved significantly due to utilization of adaptive mesh refinement technique. Moreover, design charts for an estimation of ξγ are presented for variable footing width ratios, spacings between the footings, friction angles of the subsoil and loading factors of the existing footing.

Modelling T-bar penetration in soft clay using large-displacement sequential limit analysis

T-bar penetrometers are commonly used for the measurements of undrained strength profiles for clay (e.g. intact shear strength, sensitivity, ductility). The adoption of a constant resistance factor in the absence of a full-flow failure mechanism, coupled with the strain-softening effect, usually leads to considerable underestimation of soil strength within the depth of up to several T-bar diameters. This paper presents a numerical investigation into the vertical penetration behaviour of a T-bar using a sequential limit analysis (SLA) technique. The T-bar is penetrated from the mudline to a maximum of eight diameters to capture the behaviours related to differing failure mechanisms. The robustness of the SLA is demonstrated through comparisons between lower- and upper-bound solutions and between the SLA and the coupled Eulerian–Lagrangian results, in terms of penetration resistance and failure mechanism. The influences of unit weight, strain softening and strain rate are then examined, based on which an analytical model is developed for more accurate quantification of soil strength back-calculated from T-bar penetration resistance.

Unified upper bound solution for bearing capacity of shallow rigid strip foundations generally considering soil dilatancy

In light of the upper bound method of a kinematical limit analysis, traditional log-spiral shear zones in the admissible failure mechanism of foundation soil loaded by shallow rigid strip footings are unified by introducing a nonnegative coefficient for the internal friction angle of the soil to generally reflect practical soil dilatancy. While the computed coefficient is generally between 0 and 1 to be compatible with its physical meaning, in many cases it was between 0.5 and 1. The proposed mechanism includes the traditional log-spiral and circular-arc mechanism, and is capable of determining a smaller value of the solution to the bearing capacity than some classic theoretical methods. Based on the proposed mechanism, two bearing capacity factors are refined from the traditional three factors based on the finding that the traditional factors Nq and Nc are not independent of the footing depth and soil cohesion, respectively. A formula including the two items is provided to make the proposed method convenient for use for the practical footings on homogeneous soil.

Near-optimal search-and-rescue path planning for a moving target

Discrete search and rescue path planning for a moving target problem is computationally hard. Despite heuristic methods proposed so far, for which efficiency is further plagued by random episodic target kinematic behavior, qualifying real solution goodness and specifying optimality gap still remain elusive. In this paper a new alternate formulation is proposed to solve the search path planning problem for a moving target. Rather than tackling explicitly the original problem model, a remarkable property is exploited to solve a conjugate mixed-integer linear programming problem. The approach lies on a compact open-loop search path planning problem model with anticipated feedback to efficiently minimize probability of detection failure as opposed to traditionally maximize cumulative probability of success. Preserving path solution optimality, solving the conjugate problem proves very valuable in significantly reducing computational complexity. This is mainly achievable by virtue of the resulting problem objective property which concisely defines the function to be minimized in terms of terminal belief contributions only. For the first time optimal or upper bound solution computation are made possible in reasonable time for practical size problems. A network representation is further utilized to simplify modeling and facilitate constraint specification. Computational results show the strength of the approach for one and two searching agent problem instances.

Study on vertical bearing capacity of solid and perforated mudmats in clay

As a kind of subsea shallow foundation, mudmats are widely employed to provide temporary support for jacket structures during installation and permanent support for deep-water subsea production infrastructures. Perforated mudmats are increasingly used to facilitate the installation and removal. An upper-bound solution was presented to evaluate the ultimate bearing capacity of solid and perforated mudmats. A series of model tests at 1 g and two centrifugal model tests at 100 g were conducted to examine the impact of loading rate, perforation ratio R, perforation number np and perforation shape. It was found that the bearing capacity factor Nc decreases with perforation ratio R, while the perforation number np and perforation shape only slightly affect Nc at the same R. Finally, the upper-bound method results and test results are in good agreement, which indicates the applicability of the proposed method.

CAR: heuristics for the inventory routing problem

Vendor managed inventory (VMI) is a streamlined approach to inventory and order fulfillment and is a system in which vendors continuously and automatically replenish a trading partner’s inventory. Vendors must ensure appropriate quantities of storages at the point of demand and must ensure optimal distribution plans, including routing of the distribution vehicles. This problem is known as the inventory routing problem (IRP) and seeks to integrate the routing of vehicles used for collection and distribution, with conventional inventory management. This paper addresses an IRP with a manufacturer that supplies a product using a fleet of vehicles to a set of warehouses over a defined time horizon. We develop a mixed integer linear program to determine the optimal allocation and the routing schedule for warehouses over the defined time horizon. To solve this problem, we propose a three-phase heuristic approach, called CAR: clustering of receiver nodes, allocation of quantities to these nodes, and routing of delivery vehicles through clusters of nodes. Computational studies are carried out and experimental trials conducted over a large number of data sets provide encouraging results and show usefulness of the solution approaches. The proposed ILP would provide optimal solution to the problem but it demands huge computational effort. However, CAR2, a proposed heuristic, is able to get solutions 7.41% better than the upper bound solutions obtained from CPLEX. These approaches can easily be implemented into existing VMI systems.

Face stability analysis of a shallow horseshoe-shaped shield tunnel in clay with a linearly increasing shear strength with depth

The face stability of a horseshoe-shaped shield tunnel in undrained clays with a linearly increasing strength is numerically and analytically investigated in this paper. Based on the kinematic approach of limit analysis, a continuous velocity field for a horseshoe-shaped shield tunnel is proposed to evaluate the limit support pressure of both the collapse and blow-out of the tunnel face. Moreover, the analytical results are compared with those obtained from the numerical simulation and other existing literatures. The results show that the horseshoe-shaped shield tunnel can improve the face stability compared to the circular shield tunnel. Finally, an improved velocity field is proposed, which provides a more realistic failure pattern and a better upper bound solution of the limit support pressure for the horseshoe-shaped shield tunnel.