Upper-bound Plasticity Research Articles

Edge punching shear of waffle slabs subjected to moment parallel to the slab's free edge

The test results of five one-tenth scale micro-concrete waffle slabs subjected to edge punching shear in the presence of moment transfer parallel to the slab's free edge are presented. Although the observed punching failure mechanism of the waffle slabs was found to be very similar to that of a flat slab, the shear capacity was reduced because some of the potential failure surface is lost when it extends into the waffle section. Since the current codes of practice do not specifically consider the punching shear mechanism of waffle slabs, comparisons with test results revealed that the application of various codes overestimated the punching capacities of waffle slabs. An upper-bound plasticity theory model was developed to predict the punching shear failure load. The proposed model assumes concrete to be a perfectly rigid plastic material with the modified Mohr–Coulomb failure criterion. The model showed good agreement with the test results.

The stress function basis of the upper bound theorem of plasticity

The discontinuous slip-line form of upper bound plasticity analysis is considered using an equilibrium of forces approach. It is demonstrated that the underlying basis of the approach can be written in terms of stress functions that provide a continuum stress state interpretation of the upper bound solution. An alternative proof of the upper bound theorem, applicable to both associative and non-associative materials, using stress functions is presented. The broader nature of the equilibrium form and the strict conditions under which it is valid are discussed, including examination of the apparent omission of moment equilibrium and associativity in many equilibrium form solutions. Finally, the relationship of the stress function formulation to the output of the computational limit analysis method discontinuity layout optimisation (DLO) and the potential to use the stress function formulation to derive a form of lower bound solution from an upper bound analysis are demonstrated.

Effect of loading eccentricity on the ultimate lateral resistance of twin-piles in clay

This paper studies the effect of loading eccentricity and pile spacing on the ultimate lateral soil resistance of twin-piles using finite element limit analysis and analytical upper bound plasticity methods. Two kinematic mechanisms corresponding to the failure modes produced by the advanced finite element simulations are postulated with different eccentricity and pile spacing cases. Comparisons have shown excellent agreements between the two approaches. A series of parametric studies are then subsequently performed. Numerical results have shown that loading eccentricity considerably affects ultimate lateral soil resistance, leading to a maximum reduction of 50%. In addition, the curve of normalised pile resistance versus pile spacing ratio is dissimilar to that without considering the effect of loading eccentricity. The proposed solutions and failure mechanisms in this study will provide a deepened insight on the performance of twin-pile group under eccentric loads.

Shear Capacity of Reinforced Concrete T-Beams Retrofit with Externally Bonded CFRP Fabric: A New Perspective

Unanchored U-wrapped externally bonded carbon-fiber-reinforced polymer (CFRP) fabrics are widely used to increase the design shear strength of existing reinforced concrete slab-on-beam structures, but current design models do not accurately predict the degree of enhancement. Experimental investigations further indicate that some T-beams retrofit with externally bonded CFRP fabric fail at lower shear loads than nominally identical nonretrofit reference counterparts, suggesting a negative experimental CFRP contribution. This work finds a new application for the upper-bound theorem of plasticity in analyzing the problem of U-wrapped externally bonded CFRP-retrofit beam behavior. The study provides insight into the poor historical prediction of the CFRP contribution, and demonstrates the limitations of a widely used experimental approach to determining this contribution. The analysis suggests a new way of thinking about the behavior of slab-on-beam structures retrofit with unanchored U-wrapped externally bonded CFRP. The upper-bound plastic analysis provides better predictions of retrofit shear capacity than some widely used design models, indicating that this approach can lead to better design of retrofit interventions in future. This work proposes a new design limit on enhancement that can reduce the likelihood of unsafe design in practice.

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.

A generalized mechanics theory of idealized rough surfaces under dry and liquid-mediated plastic contact conditions

An upper-bound plasticity analysis based on volume conservation and presumed uniform surface rise of noncontact regions was used to develop analytical models of a rigid-perfectly plastic half-space with a flat surface indented by a sinusoidal rigid surface and a rigid-perfectly plastic half-space with a sinusoidal surface compressed by a rigid flat surface. The hydrodynamic effect of lubricant fluid pressurized in the surface grooves of the deformed half-space on the deformation process was analyzed by solving the Reynolds equation of a squeezed film using a perturbation method. Analytical solutions of the fractional contact area, normal approach, average surface rise, cavity volume, and surface roughness were obtained after plastic contact deformation. Numerical results of a finite element analysis of relatively compliant and stiff elastic-nearly perfectly plastic materials are shown to be in good agreement with analytical results. The hypothesis of uniform surface rise of noncontact regions is shown to be a reasonable assumption, leading to a good approximation of global deformation quantities and providing an accurate description of changes in the surface profile for relatively large contact areas. The results of the present study provide a basis for explaining the full plastic merger of asperity contacts in multi-scale rough (fractal) surfaces and elucidate the role of surface roughness in metal-working processes.

Seismic bearing capacity of surficial foundations on sloping cohesive ground

Engineers often assume undrained conditions in stability calculations of shallow foundations resting on soil with fine content as this assumption yields conservative results. Calculation of undrained bearing capacity of shallow foundations on level ground is a well-defined problem and when the footing is located on or near slopes, empirical equations or design charts produced based on limit equilibrium, upper bound plasticity calculations or finite element method (FEM) analyses are used. On the other hand, available studies that consider seismic bearing capacity of foundations on cohesive soils do not consider the influences of all influential parameters. Therefore, their use in design practice is rather limited. Accordingly, this study attempts to develop design charts that consider the influences of all parameters that affect the undrained bearing capacity factor of surficial strip footings under seismic conditions (Ncse). These influences are footing width, slope angle, slope height, footing position, undrained shear strength and pseudo-static acceleration coefficient. As the number of parameters to be considered is high, a parametric study is conducted using FEM models. Obtained results are consistent with the results of available studies in literature. Proposed design charts allow the selection of problem specific Ncse values. A design procedure is defined and two design examples are presented for the calculation of the magnitude of undrained bearing capacity under seismic conditions.

An analytical solution for the undrained horizontal–torsional resistance of mudmats

Rectangular mudmat foundations are frequently used for supporting subsea structures for offshore oil and gas developments. The self-weight of the subsea structure and mudmat often mobilise a relatively small proportion of the vertical bearing capacity and horizontal–torsional sliding generally represents the governing load case. However, the effect of torsion on mudmat capacity is not explicitly considered in current guidelines for geotechnical design of offshore foundations. In this paper, upper-bound plastic limit analysis is used to develop explicit expressions for the combined horizontal and torsional capacity of skirted mudmats. The results of the limit analyses are compared with results from finite-element analysis, and with other published solutions. A method is proposed for estimating the translational sliding resistance from the interaction diagram for biaxial horizontal loading and a unique expression is proposed to define the normalised H–T failure envelope. The effects of foundation aspect ratio, foundation embedment ratio, skirt–soil interface roughness, direction of horizontal loading and degree of soil strength heterogeneity are investigated systematically.

Investigation of headed bar joints between precast concrete panels

The paper addresses the design and behaviour of narrow cast in-situ joints between precast concrete elements in which continuity of reinforcement is achieved through overlapping headed bars. Using headed bars minimises the lap length required within the cast-in-situ joint region. Confining reinforcement in the form of transverse bars and vertical shear studs is also installed in the joint. The paper describes a series of tensile tests which were carried out to simulate the tensile zone of a joint loaded in pure flexure. The headed bars used in the tests were 25mm in diameter with 70mm square heads and yield strength of 530MPa. The tests studied the influences of concrete strength, headed bar spacing, splice length, transverse reinforcement and confining shear studs on joint strength. A lap length of 100mm in concrete with 28MPa cylinder strength was found to be sufficient to develop the full strength of the headed bars. A strut-and-tie model (STM) is presented for determining joint strength. Analysis shows that the STM gives safe results even though it does not fully capture the observed joint behaviour. An upper bound plasticity model is found to give relatively good predictions of joint strength in most cases, although it also does not always capture the correct failure mechanism. The tests provide insights into joint behaviour which, in conjunction with numerical modelling, will facilitate the development of an improved design method. Widespread use of this system would lead to improvements in buildability, sustainability and health and safety in the construction of concrete structures.

Capacity of rectangular mudmat foundations on clay under combined loading

Rectangular shallow foundations known as mudmats are commonly used in the offshore oil and gas industry. They are often subject to large horizontal forces that can also give rise to overturning and torsional moments. This paper focuses on analysing the ultimate capacity of a rigid rectangular mudmat resting on the surface of, or embedded in, homogeneous undrained clay. Realistic three-dimensional load combinations are applied, based on the combined horizontal, moment and torsional loading generated by a horizontal force applied within the envelope of the mudmat and the equipment that it supports. Analytical lower- and upper-bound plasticity calculations are performed for a surface footing under combined horizontal and torsional loading, while embedded footings and more complex loading arrangements are considered using three-dimensional finite-element limit analysis. The undrained soil is modelled as a rigid–plastic von Mises material, and the interface between the external sides of the mudmat and the soil is modelled with both unlimited and zero tension capacity. Design charts are presented and relationships between loading combinations and failure mechanisms are explored.

Ultimate lateral bearing capacity of tetrapod jacket foundation in clay

The tetrapod jacket foundations that are always used to support offshore wind turbines have been investigated primarily in laboratory experiments. In this study, the ultimate lateral soil resistance on this type of foundation was investigated using the finite element method and the analytical upper bound plasticity method. The numerical results show good agreement with the theoretical upper bound solutions under the same pile spacings (S) and soil-pile adhesion factors (α). Three distinct failure mechanisms (mechanisms A, B and C) were established in terms of different pile spacings. The ultimate lateral pressure was subsequently determined using numerical analyses with consideration of the loading direction. The most critical loading direction angles (θ) vary with the soil-pile adhesion factors, and are θ=0 for α=1 and θ=π/4 for α=0. Selected empirical equations were proposed to predict the ultimate lateral bearing capacity for engineering practice, considering the pile spacing, soil-pile adhesion and loading direction.

Shape Effects on the Undrained Uplift Capacity of Skirted Suction Foundations in Clay

Skirted suction foundations are an attractive solution for floating offshore wind turbines that are subject to uplift due to overturning or buoyancy loading. Current industry design guidelines give conservative collapse loads for offshore shallow foundation systems, particularly due to neglecting the beneficial effect of suction developed within the soil plug during rapid uplift. The behavior of skirted rectangular and circular footings subjected to uplift loading has been studied using centrifuge model tests and upper bound plastic limit analyses. Results demonstrate that the shape effects on the uplift capacity factor are not significant when the circular and rectangular footings both obey reverse end bearing failure mechanism. Simple predictive methods based on existing bearing capacity theory are provided.

Undrained limiting lateral soil pressure on a row of piles

The displacement finite element, lower and upper bound finite element limit analysis and analytical upper bound plasticity methods are employed to investigate the undrained limiting lateral resistance of piles in a pile row. Numerical analyses and analytical calculations are presented for various pile spacings and pile–soil adhesion factors. The numerical results are shown to be in excellent agreement with each other and also with the theoretical upper bounds produced by the analytical upper bound calculations. Based on the numerical and analytical results, an empirical equation is proposed for the calculation of the ultimate undrained lateral bearing capacity factor. This equation is subsequently used to calculate p-multipliers applicable to the lower part of piles in pile rows, which are compared to multipliers available in the literature (that are constant with depth). The comparison shows significant differences, indicating that the amount of reduction in lateral resistance due to group effects is not constant with depth as routinely assumed in practice.

Analysis of Bearing Capacity of Suction Bucket Foundation Subjected to Horizontal and Moment Loadings

The suction bucket foundation is not only supporting the vertical loading such as the sea platform and weight itself, but also subjecting to horizontal and moment loading due to wind and wave. The response of bucket foundation to combined Horizontal (H) and Moment (M) loading has been studied using 3D finite element analysis Then the proposed method is numerically implemented in the framework of the general-purpose FEM software ABAQUS. Relationship curve between the coefficient of ultimate bearing capacity and displacement is obtained by the application of load-displacement controlled method in homogeneous soft foundation the failure envelope of foundation in the M-H is obtained by the application of swipe testing. The behavior is explained using upper bound plasticity mechanisms suggested by the soil deformation mechanisms observed in the finite element analysis. The numerical results computed by the proposed method will be helpful in engineering practices.

Ultimate lateral pressure of two side-by-side piles in clay

The ultimate earth resistance for a group of two side-by-side piles that are laterally loaded in clay is investigated using four different methods of analysis: three numerical (the displacement finite-element method, and the upper- and lower-bound finite-element limit analysis methods) and one analytical (an analytical upper-bound plasticity method developed in this paper). The results of the three numerical methods are shown to be in excellent agreement, while the analytical solution presents a theoretical upper bound that is very close to the numerical results. The results of the analyses are used to identify the predominant failure mechanisms for different pile spacings and pile–soil adhesions. They are also used to develop a design chart and design equations for determination of the ultimate lateral bearing capacity factor.

Tests and limit analysis of loop connections between precast concrete elements loaded in tension

This paper deals with loop connections loaded in tension. Such connections; also known as U-bar joints, are frequently used in practice to establish continuity between precast deck elements in steel–concrete composite bridges. The tensile strength of a loop connection may either be governed by yielding of the U-bars or by failure in the joint concrete. Only few investigations of the case of concrete failure can be found in the literature. This paper presents an experimental program dedicated to study loop connections critical to concrete failure. The results show that the ultimate load is influenced by important design parameters such as the overlapping length of the U-bars, the spacing between adjacent U-bars and the amount of transverse reinforcement. Knowledge about the parameters that have an effect on the failure of the joint concrete is important in order to avoid this failure mode in practice. The paper also presents an upper bound plasticity model, which is able to capture the experimental tendencies in a satisfactory manner. Finally, the paper includes discussions of how the presented research may be utilized in practice to design connections that are able to transfer the full yield strength of the connecting precast elements.

Influence of deformation inhomogeneity on the annealing behavior of drawn oxygen-free high conducting copper

Abstract

Closely correlating lower and upper bound plastic analysis of real slabs

Engineers assessing existing reinforced concrete slabs sometimes use plastic analysis to prove that the slabs are stronger than suggested by simple elastic methods. This approach allows engineers to avoid unnecessary strengthening and replacement work. The 'yield line' form of plastic analysis is particularly appealing because its results can be easily understood and checked. However, careless application of the method to complicated real slabs can produce 'unsafe' results. Many recent 'safe' alternatives are harder to interpret and to check. This paper presents a new technique which eliminates the previous disadvantages of yield line analysis to ensure a safe and accurate result, but which remains easy to understand and check. When applied to real structures, the method allows engineers to apply powerful plastic theory whilst remaining confident in their results.

Limit analysis of the undrained bearing capacity of offshore pipelines

The ultimate bearing capacity of a rigid, plane-strain pipe segment embedded in undrained clay is studied using numerical limit analysis. The pipe is considered to be ‘wished in place' at invert penetrations ranging from zero to five pipe diameters, thus providing coverage of both on-bottom (partially embedded) and trenched (fully embedded) offshore pipelines. The soil is modelled as a rigid-plastic Tresca material with either uniform strength or strength proportional to depth. The effects of soil weight, interface roughness and interface tensile capacity are investigated in a systematic manner. All calculations are performed using the finite-element limit analysis code OxLim, which uses adaptive mesh refinement to compute tightly bracketed lower- and upper-bound plasticity solutions. The velocity fields from the upper-bound analyses provide the corresponding failure mechanisms. The paper initially focuses on purely vertical loading (penetration and uplift), and then addresses combined vertical and horizontal loading. A comprehensive set of design curves and failure envelopes is presented, with the results explained in terms of the changing failure mechanisms. These results are immediately applicable in practice. In particular, current industry-standard procedures for design against pipeline upheaval are critically reviewed, and are shown to have potentially unconservative shortcomings.

Collapse mechanisms and strength prediction of reinforced concrete pile caps

This paper describes an upper bound plasticity approach for strength prediction of reinforced concrete pile caps. A number of collapse mechanisms are identified and analysed. The procedure leads to an estimate of the load-carrying capacity and an identification of the critical collapse mechanism. Calculations have been compared with nearly 200 test results found in the literature. Satisfactory agreement has been found. The analyses are conducted on concentrically loaded caps supported by four piles. The paper briefly outlines how the approach may be extended to more complicated loadings and geometries. It is argued that the upper bound approach may be a useful complement to the widely used lower bound strut-and-tie method. Especially when dealing with strength assessment of existing structures.