Upper-bound Theory Research Articles

Seismic Design of Buckling-Restrained Brace in Preventing Local Buckling Failure

When a buckling-restrained brace (BRB) is composed of a flat steel core encased in a rectangular steel tube with infill mortar, the flat steel core develops high-mode buckling waves within the spaces occupied by compressible debonding layers when BRB is in compression. The wave crests and troughs collide with mortar and then acting outward forces on restrainer. The steel tube wall may bulge out if the restrainer is too weak to sustain the outward forces and the BRB may lose its compression carrying capability. The outward force can be estimated according to steel core high-mode buckling wavelength and the debonding layer thickness. The restrainer capacity in resisting outward forces can be estimated by using the upper bound theory in plastic analysis. The results of 39 BRB tests were compared in order to evaluate the effectiveness of steel tube capacity estimation methods. 24 BRBs exhibiting local bulging failure suggested that the steel tube capacity can be estimated by assuming the bulged wall as a wedge shape with five of its boundary developing flexural strength. The proposed estimation is conservative and can be adopted for BRB design in preventing local bulging failure for severe seismic services.

Revisiting crown stability of tunnels deeply buried in non-uniform rock surrounds

A kinematic analysis procedure is presented to investigate the crown stability of deep-buried tunnels in non-uniform rock strata. The non-uniformity of rock properties is considered using the discretized approach with finite thickness layers. In the realm of upper bound theory, kinematic analysis is briefly presented for a single layer so as to provide basis for multi-layer analysis. A 2D collapse mechanism is postulated to depict the potential falling block with an arbitrary tunnel cross-section, although rectangular tunnels are considered in the 3D kinematic analysis for ease of calculation. An impending collapse is likely to occur, provided that the width of the excavation is no less than the collapse width. In order to reflect the nonlinear characteristics of rock materials at failure, the Hoek-Brown criterion is employed for tightly interlocked and very poor rock masses, with its form expressed by normal and shear stresses to facilitate calculations of internal energy dissipation rate. Based on the variational principle and power-based balance equation, the effective collapse mechanism is derived in closed form. Comparison is carried out to verify the robustness of the proposed approach. Sensitivity analysis is performed to depict the influence of each non-uniform rock strength parameter on crown stability. As expected, such a discretized approach incorporated into kinematic analysis enables one to account for non-uniformity of rock surrounds, which would fill the knowledge and design gap of similar tunnelling issues much needed at present state of practice.

Investigation of the effect of surcharge on behavior of soil slopes

By increase in the population and consequently constructions, new structures may be built in vicinity of the soil slopes. Such structures can be regarded as an extra surcharge on the slopes. The intensity and location of the surcharge affects the displacements of the slopes. Few researchers have studied the effect of surcharge on displacements of soil slopes. In this research, using limit analysis method and upper bound theory with non-associated flow rule, displacements of soil slopes in vicinity of a surcharge has been estimated. The authors have improved the technique previously proposed by them and a new formulation is suggested for calculating the permanent displacements of the soil slope in presence of a surcharge for two failure modes, rotational and transitional. A comparison has also been made between the two mentioned modes for various conditions of surcharge and slope. The conditions resulting in the rotational mode to be more critical than the transitional mode have been investigated. Also, the effects of surcharge\'s intensity, location of surcharge as well as the soil properties have been investigated.

Application of T-bar in numerical simulations of a monopile subjected to lateral cyclic load

ABSTRACTA series of centrifuge tests were performed to investigate the response of a free-head monopile due to cyclic lateral loading in normally consolidated clay. By linking the maximum reaction-force point of the final cycles in all tests with various amplitudes, a postcyclic reaction-force curve is obtained, which can be used to assess the postcyclic remolded lateral stiffness. To numerically analyze the tests, a strength degradation model of the clay is calibrated by the T-bar cyclic test. However, this model is T-bar-dependent, which is unable to capture the degrading behavior of the monopile stiffness. Thus, a modification approach is proposed based on the upper bound theory, and the modified model is further combined with finite element analysis to simulate the cyclic behavior of the model pile. The simulation results show similar degrading trend and consistent postcyclic remolded lateral stiffness with the model tests. This further demonstrates that the remolded lateral stiffness mainly depends on the soil remolded strength, which is one of the parameters calibrated by the T-bar tests. Based on this finding, a simplified numerical analysis is proposed, which can predict the postcyclic reaction-force curve by performing one monotonic loading instead of modeling the whole process of cyclic loading.

An upper bound theory to approximate the natural frequencies and parameters identification of composite beams

For the free vibration of composite beams and non-uniform beams we propose a new upper bound theory to approximate the first few natural frequencies. The Rayleigh quotient is expressed in terms of boundary functions, instead of that in terms of eigenfunctions. The boundary function satisfies all boundary conditions of the given beam, and is at least the fourth-order polynomial with leading coefficient to be one. We prove that the maximality of the Rayleigh quotient in the space of the kth order boundary functions is equivalent to the orthogonality of the kth order boundary function to lower order optimal boundary functions. Hence, we can easily find the kth order natural frequency through an orthogonalization technique provided. When the first three natural frequencies are compared with the exact or numerically found ones, good results are obtained, which confirm the applicability of the present upper bound theory. We address the inverse problems of composite beam equations, where we use the orthogonal system of boundary functions as bases to expand the unknown functions and derive linear algebraic equations to determine the expansion coefficients. As a consequence, we can fast and accurately estimate the unknown rigidity function and planar inertial function with the help of the first three natural frequencies, and the supplemented measured data of recovered function on two boundaries. The robustness of the present inversion methods is demonstrated by numerical examples.

Upper bound analysis for bearing capacity of nonhomogeneous and anisotropic clay foundation

The bearing capacity calculations for nonhomogeneous and anisotropic clay foundation are often employed the methods of limit equilibrium, limit analysis and characteristic. In this paper, an approach of upper bound theorem in conjunction with new failure mechanism is adopted to estimate the bearing capacity of foundation in nonhomogeneous and anisotropic clays. The proposed failure mechanism is composed of a series of rigid blocks, which is constructed in a manner to respect the normality condition of limit analysis theory at every point of velocity discontinuity surfaces, considering the property of spatially varying materials. Using a spatial discretization technique, the slip surface of failure mechanism is determined point by point. Based on upper bound theory of limit analysis, the internal energy dissipation and the work rate of external forces are calculated for each block. Coding the corresponding computer program, the solutions of bearing capacity of nonhomogeneous and anisotropic clay foundation are obtained. The results are compared with those previously published solutions using the characteristic and limit equilibrium methods. From the comparisons, it is found that the approach of this paper is effective to analyze the bearing capacity of nonhomogeneous and anisotropic clays. Then, the solutions are presented, and the influence of nonhomogeneity and anisotropy on the bearing capacity is discussed.

The research of design method for anchor cables applied to cavern roof in water-rich strata based on upper-bound theory

In this study, we use the upper-bound method to develop a collapse failure mechanism of the roof surrounding rock of semicircle arched roadway, with a consideration of the water pressure in the stratum and the support from anchor cables. We consider a cavern with a semi-circular roof and straight walls in a water-rich stratum as a case study. A design method is presented for the required length of and the pre-tightening force of anchor cables on the cavern roof, based on the Hoek–Brown criterion. We analyse the effects of factors such as the cavern width, the pore-water pressure coefficient and the specific weight and the compressive and tensile strengths of the rock mass using established sensitivity indexes for the factors that affect the design parameters of anchor cables. We provide recommendations for controlling the surrounding rock in practical engineering applications for actual scenarios. The design method is used to determine the parameters of anchor cables for the roof of a primary drainage pump station in a mine. The designed anchor cables are used to effectively control the deformation of the surrounding rock. The results show that at the early stage of the excavation of a cavern, the collapse of the surrounding rock of the roof can only be effectively controlled using anchor cables with lengths that meet the design requirements and to which a sufficient pre-tightening force has been applied. In addition, the required length of anchor cables increases with the cavern width, the pore-water pressure coefficient and the specific weight of the rock mass and decreases as the compressive strength of the rock mass increases. The cavern width has the highest sensitivity among the influence factors for the length of anchor cable. Furthermore, the required pre-tightening force for anchor cable for the roof decreases as the tensile and compressive strengths of the rock mass increase and increases with the pore-water pressure coefficient, the cavern width and the specific weight of the surrounding rock. The cavern width also has the highest sensitivity among the influence factors for the pre-tightening force. Finally, the cavern shape and width should be carefully selected for the design and construction of a cavern with weak surrounding rock in a water-rich stratum. The intactness of the surrounding rock should be improved by using high-strength and high-toughness anchored supporting components, applying a high pre-tightening force to the anchored supporting components and using grouting reinforcement to mitigate the effect of water. In this way, relatively good control of the surrounding rock can be realised.

帯板形式の組立圧縮材の座屈と骨組の座屈の関連性について

1. Introduction The objective of this study is to examine the relationship between battened built-up columns and frames about buckling. Especially, the characteristics of the Bleich's formula are investigated with respect to the upper bound theory and moment distribution. The buckling strengths, buckling modes and bending moment of one bay －n stories frame with rigid beams are calculated by the energy method. The results are compared with those of obtained by the Bleich's formula and correct solutions. 2. Analytical work The analytical model is shown in figure 3. Buckling strengths are calculated by the three methods. Firstly, the buckling formula presented by Bleich is shown, and analytical method using the energy method is described, where the buckling modes are assumed by the equations (12). The buckling equation is presented as equations (22). Moreover it is shown that the correct buckling strengths can be calculated by the equations (23) and (24). 3. Results and Discussion As the analytical parameters, the number of stories n and the value of 4Ic/Acb2 are selected. The values of n are 1, 2, 3, 5, 10 and the value of 4Ic/Acb2 ranges from zero to one. Figure 5 and 6 show the correct dimensionless buckling strength p*-4Ic/Acb2 relations and pg*-4Ic/Acb2 relations. Figure 8 shows the ratio of the Bleich's strength to the correct value and the strength obtained by the energy method to the correct value. Although the buckling strengths by Bleich agree fairly well with correct values, it is shown that the strengths obtained by Bleich equation are neither the upper bound nor the lower bound. Moreover, Figure 12 shows that Bleich's moment distributions correspond to those of obtained by the energy method. 4. Conclusions The conclusions derived from this study are as follows: 1) Governing parameters of the problem are the number of story n and the value of 4Ic/Acb2. 2) Although the buckling strengths by Bleich agree fairly well with correct values, the strengths by Bleich are neither the upper bound nor the lower bound. 3) Buckling strengths calculated by the energy method estimate the correct strength within 5% error in case of n>2. As is well known, the buckling strength by the energy method gives the upper bound. 4) Bleich's moment distributions correspond to those of obtained by the energy method.

Upper bound analysis for deep tunnel face with joined failure mechanism of translation and rotation

A joined failure mechanism of translation and rotation was proposed for the stability analysis of deep tunnel face, and the upper bound solution of supporting force of deep tunnel was calculated under pore water pressure. The calculations were based on limit analysis method of upper bound theory, with the employment of non-associated Mohr-Coulomb flow rule. Nonlinear failure criterion was adopted. Optimized analysis was conducted for the effects of the tunnel depth, pore water pressure coefficient, the initial cohesive force and nonlinear coefficient on supporting force. The upper bound solutions are obtained by optimum method. Results are listed and compared with the previously published solutions for the verification of correctness and effectiveness. The failure shapes are presented, and results are discussed for different pore water pressure coefficients and nonlinear coefficients of tunnel face.

Seismic design and testing of buckling‐restrained braces with a thin profile

SummaryA thin‐profile buckling‐restrained brace (thin‐BRB) consists of a rectangular steel casing and a flat steel core that is parallel to a gusset plate. A thin configuration reduces the width of the restraining member and thus saves usable space in buildings. However, deformable debonding layers, which cover the steel core plate in order to mitigate the difference between the peak tensile and compressive axial forces, provide a space for the steel core to form high mode buckling waves when the thin‐BRB is under compression. The wave crests squeeze the debonding layers and produce outward forces on the inner surface of the restraining member. If the restraining member is too weak in sustaining the outward forces, local bulging failure occurs and the thin‐BRB loses its compression capacity immediately. In order to investigate local bulging behavior, a total of 22 thin‐BRB specimens with a ratio of steel core plate to restraining steel tube depth ranging from 0.3 to 0.7 and axial yield force capacities ranging from 421 kN to 3036 kN were tested by applying either cyclically increasing, decreasing, or constant axial strains. The restraining steel tube widths of all the specimens were smaller than 200 mm and were infilled with mortar with a compressive strength of 97 MPa or 55 MPa. Thirteen of the 22 thin‐BRB specimens' restraining members bulged out when the compressive core strains exceeded 0.03. A seismic design method of the thin‐BRB in preventing local bulging failure is proposed in this study. Test and finite element model (FEM) analysis results suggest that the outward forces can be estimated according to the BRB compressive strength, steel core high mode buckling wavelength, and the debonding layer thickness. In addition, the capacity of the restraining member in resisting the outward forces can be estimated by using the upper bound theory in plastic analysis. Both the FEM analysis and test results indicate that the proposed method is effective in predicting the possibility of local bulging failure. Test results indicate that the proposed design method is conservative for thin‐BRB specimens with a large steel core plate to restraining steel tube depth ratio. This paper concludes with design recommendations for thin‐BRBs for severe seismic services. Copyright © 2015 John Wiley & Sons, Ltd.

Base stability analysis of braced deep excavation in undrained anisotropic clay with upper bound theory

It is imperative to evaluate factor of safety against basal heave failure in the design of braced deep excavation in soft clay. Based on previously published field monitoring data and finite element analyses of ground settlements of deep excavation in soft clay, an assumed plastic deformation mechanism proposed here gives upper bound solutions for base stability of braced deep excavations. The proposed kinematic mechanism is optimized by the mobile depth (profile wavelength). The method takes into account the influence of strength anisotropy under plane strain conditions, the embedment of the retaining wall, and the locations of the struts. The current method is validated by comparison with published numerical study of braced excavations in Boston blue clay and two other cases of excavation failure in Taipei. The results show that the upper bound solutions obtained from this presented method is more accurate as compared with the conventional methods for basal heave failure analyses.

Seismic Bearing Capacity of Strip Footings Located Close to the Crest of Geosynthetic Reinforced Soil Structures

This paper investigates the performance of geo-reinforced soil structures subjected to loading applied to strip footings positioned close to a slope crest. The kinematic theorem of limit analysis, which is based on the upper bound theory of plasticity, is applied for evaluating the ultimate bearing capacity within the framework of pseudo-static approach to account for earthquake effects. The mechanism considered in this analysis is a logarithmic spiral failure surface, which is assumed to start at the edge of the loaded area far from the slope, consistent with the observed failure mechanisms shown in the experimental tests reported in the literature. A parametric study is then carried out to investigate the influence of various parameters including the geosynthetic configuration, backfill soil friction angle, footing distances from the crest of the slope, slope angles and horizontal seismic coefficients. Attention is paid to the failure mechanism because its maximum depth is the depth at least to which the reinforcements must be placed. Results of the analyses are presented in the form of non-dimensional design charts for practical use. Finally, a simple procedure based on the assessment of earthquake-induced permanent displacements is shown for the design of footing resting on reinforced slopes subjected to earthquake.

Reliability analysis of retaining walls with multiple failure modes

In order to reduce the errors of the reliability of the retaining wall structure in the establishment of function, in the estimation of parameter and algorithm, firstly, two new reliability and stability models of anti-slipping and anti-overturning based on the upper-bound theory of limit analysis were established, and two kinds of failure modes were regarded as a series of systems with multiple correlated failure modes. Then, statistical characteristics of parameters of the retaining wall structure were inferred by maximal entropy principle. At last, the structural reliabilities of single failure mode and multiple failure modes were calculated by Monte Carlo method in MATLAB and the results were compared and analyzed on the sensitivity. It indicates that this method, with a high precision, is not only easy to program and quick in calculation, but also without the limit of nonlinear functions and non-normal random variables. And the results calculated by this method which applies both the limit analysis theory, maximal entropy principle and Monte Carlo method into analyzing the reliability of the retaining wall structures is more scientific, accurate and reliable, in comparison with those calculated by traditional method.

Investigation of Bearing Strength of Single-Bolt Double-Lap Joints in Composite Laminate

Based on the Upper Bound Theory, a Simplified Engineering Approach is Presented to Determine the Ultimate Strength of a pin-Loaded Composite Laminate in this Papaer. According to the Upper Bound Theory, the Displacement Rate in a Given Ply is Divided into Two Zones: the Moving Zone and the Static Zone. the Applied Load Q that Associated with Displacement must be Less than the Maximum Resistance of the Laminate. in this Paper we have Discussed the Failure Region, Failure Type of each Ply and Simplified the Tsai-Wu Failure Criterion. Experiments of Single-Bolt Double-Lap Joints have been Conduncted According to ASTM D5961 Test Standard. Finally, we can Observe that the Engineering Approach is in Good Agreement with the Test Results.

Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection

Direct numerical simulation (DNS) has shown that Rayleigh–Bénard convection in a fluid-saturated porous medium self-organizes into narrowly spaced plumes at (ostensibly) asymptotically high values of the Rayleigh number Ra . In this Letter a combination of DNS and upper bound theory is used to investigate the dependence of the Nusselt number Nu on the domain aspect ratio L at large Ra . A novel algorithm is introduced to solve the optimization problems arising from the upper bound analysis, allowing for the best available bounds to be extended up to Ra ≈ 2.65 × 10 4 . The dependence of the bounds on L ( Ra ) is explored and a “minimal flow unit” is identified. • DNS is used to quantify the aspect-ratio ( L ) dependency of Nu ( Ra ) in porous medium convection. • A “minimal flow unit” for porous medium convection is identified. • Rigorous upper bounds on Nu ( Ra ) are computed as a function of L for Ra ⩽ 2.65 × 10 4 . • A numerical scheme is developed for solving upper bound variational problems without continuation.

A limit analysis approach to derive a thermodynamic damage potential for non-linear geomaterials

This paper introduces a mathematical model which describes the continuum damage of non-linear geo-materials. The model accounts for full thermo-mechanical coupling as well as irreversible failure and its effect on shear heating. It involves multi-mechanisms creep to describe the material rheology depending on time, temperature, pressure and water content. This coupled thermo-mechanical model combined with the upper bound theory is used to formulate a potential capable of predicting the damage evolution. The model is implemented and applied to a cross-sectional geological layer subjected to extension. It reveals that damage accelerates the creation of faults and accentuates the localization of shear zones, thereby competing with the increase in material rigidity due to rate dependency, especially at high temperature.

A new analytical method for calculating seismic displacements in reinforced retaining walls

ABSTRACT: Calculating the seismic displacement of reinforced retaining walls is important for optimal design of these structures. Using the limit analysis theorem, in this study an innovative approach has been proposed for calculating the coefficient of yield acceleration and permanent displacements of geosynthetic-reinforced soil-retaining walls with full-height rigid concrete facing (GRS-FHR walls). In this manner, based on the upper-bound theory of limit analysis and Newmark's sliding block theory, a group of charts has been proposed to estimate the permanent sliding displacements and the coefficient of yield acceleration for this type of wall. In these charts, the effect of the following parameters on the magnitude of permanent displacements and on the coefficient of yield acceleration of the wall has been investigated: vertical spacing of reinforcements; ratio of width to height of facing; ratio of length of reinforcements to height of facing; and internal friction angle of the soil. Results obtained from the suggested method have been compared with the sliding displacements reported by other researchers as well as those measured at the toe of a well-known GRS-FHR wall called Tanata under the Kobe earthquake (Japan, 1995). The suggested charts are believed to provide an appropriate, handy tool for estimating the coefficient of yield acceleration and permanent sliding displacements of GRS-FHR retaining walls.

Study on the Critical Height of Homogeneous Clay Slope

Small cohesion clay slope is possible to slide along the plane slip surface or log-spiral slip surface. Based on the upper bound theory and energy principle, this paper deduced the critical height of the inclined top clay slope. The sliding mode of plane slip surface and log-spiral slip surface is studied. Finally, an engineering example is analyzed and the critical height calculation is introduced.

A Simplified Calculation Method for Spatial Effect in Large-Long-Deep Foundation Pit and its Analysis

According to the research status of construction spatial effects in large-long-deep foundation pit: mainly focus on numerical simulation, but theoretical research is not too many by now, a simplified method for calculating the construction spatial effects of large-long-deep foundation pit in cohesive soil was advanced. The soil layers around deep foundation pit were equal to cohesion-less isotropic soil mass by introducing the concept of equivalent internal friction angle. And then, by means of limit equilibrium analysis method combined with soil plasticity upper bound theory and associated flow rule, the spatial effects of two 3D failure modes: tension crack-shear and pure shear in deep foundation pit was studied concretely, and the corresponding formulas of spatial effects coefficient were put forward, also two examples were analyzed. The research results indicates that the method, which can complete by hand-calculation, avoids the defects of low efficiency, high cost and long period in numerical simulation, and the distribution characteristics and value size of spatial effects coefficient could be obtained directly from its calculation results, which can be used as guidance for the supporting structure, construction scheme design and the test points or sections choice in process of information monitoring.

INVESTIGATION MEASUREMENT OF DISPERSION COEFFICIENT AND MIXING TIMES IN BUBBLE COLUMN

A complete model of liquid-phase dispersion was used to simultaneously characterize axial and radial mixing in bubble column of 0.15 m inside diameter and plastic plate distributor with holes of 2 mm diameter. Axial and radial dispersion coefficients and mixing times were determined in tap water for superficial gas velocities in the range 0.6-5.36 cm/s. The experiments were carried out using a transient method (the tracer response method). The dispersion coefficient was obtained by adjusting the experimental profiles of tracer concentration with the predictions of the model. The measured axial dispersion coefficients (Dax,L) were generally consistent with the predictions of the well established correlations, thus validating the complete dispersion model used in the analysis. The Dax,L values ranged from 110 to 200 cm2/s. There was evidence that the existing literature data on Dax,L in bubble columns are slightly underestimated, as consistent underestimation was found to be a characteristic of the widely used dispersion model that disregards radial dispersion. The value of the radial dispersion coefficient was typically about 1 to 2% of the Dax,L value under any given condition. The mixing time data were generally consistent with the existing literature.
 The results of this study are compared with experimental result and upper bound theory and have shown a good agreement with a minimum discrepancy