Lateral earth pressure of granular backfills on retaining walls with expanded polystyrene geofoam inclusions under limited surcharge loading

Existing studies have focused on the behavior of the retaining wall equipped with expanded polystyrene(EPS)geofoam inclusions under semi-infinite surcharge loading rather than limited surcharge loading.In this paper,the failure mode and the earth pressure acting on the rigid retaining wall with EPS geofoam inclusions and granular backfills(henceforth referred to as EPS-wall),under limited surcharge loading are investigated through two-and three-dimensional model tests.The testing results show that different from the sliding of almost all the backfill in the EPS-wall under semi-infinite surcharge loading,only an approximately triangular backfill slides in the wall under limited surcharge loading.The distribution of the lateral earth pressure on the EPS-wall under limited surcharge loading is non-linear,and the distribution changes from the increase of the wall depth to the decrease with the increase of the limited surcharge loading.An approach based on the force equilibrium of a differential element is developed to predict the lateral earth pressure behind the EPS-wall subjected to limited surcharge loading,and its performance was fully validated by the three-dimensional model tests.

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio （EBR）,and the elastic modulus reduction method （EMRM） is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method.

Fatigue Life Prediction under Service Load Considering Strengthening Effect of Loads below Fatigue Limit

Lightweight design requires an accurate life prediction for structures and components under service loading histories. However, predicted life with the existing methods seems too conservative in some cases, leading to a heavy structure. Because these methods are established on the basis that load cycles would only cause fatigue damage, ignore the strengthening effect of loads. Based on Palmgren-Miner Rule （PMR）, this paper introduces a new method for fatigue life prediction under service loadings by taking into account the strengthening effect of loads below the fatigue limit. In this method, the service loadings are classified into three categories： damaging load, strengthening load and none-effect load, and the process for fatigue life prediction is divided into two stages： stage I and stage II, according to the best strengthening number of cycles. During stage I, fatigue damage is calculated considering both the strengthening and damaging effect of load cycles. While during stage II, only the damaging effect is considered. To validate this method, fatigue lives of automobile half shaft and torsion beam rear axle are calculated based on the new method and traditional methods, such as PMR and Modified Miner Rule （MMR）, and fatigue tests of the two components are conducted under service loading histories. The tests results show that the percentage errors of the predicted life with the new method to mean life of tests for the two components are –3.78% and –1.76% separately, much lesser than that with PMR and MMR. By considering the strengthening effect of loads below the fatigue limit, the new method can significantly improve the accuracy for fatigue life prediction. Thus lightweight design can be fully realized in the design stage.

Analytic Solution of Elasto-Plastic Stress in Infinite Slope under Uniform Load

According to the Mohr-Coulomb yield criterion, the stress field of the infinite slope is derived under a vertical uniform load q on the top of the slope. It is indicated that elastic and elasto-plastic states would occur in the slope. When q is smaller than the critical load, q(p), the slope is in the elastic state. If q equals q(p), the slope is in the critical state, and the plastic deformation would occur along the critical angle. With the increase of q, the plastic zone would extend, and the slope is in the elasto-plastic State. If q equals limit load, the slope is in the limit equilibrium state. The slope may be divided into three zones. Some charts of the critical angle, the critical and limit load coefficients are presented in this paper.

PLASTIC LIMIT LOAD ANALYSIS OF DEFECTIVE PIPELINES

The integrity assessment of defective pipelines represents a practically important task of structural analysis and design in various technological areas,such as oil and gas indus- try,power plant engineering and chemical factories.An iterative algorithm is presented for the kinematic limit analysis of 3-D rigid-perfectly plastic bodies.A numerical path scheme for radial loading is adopted to deal with complex multi-loading systems.The numerical procedure has been applied to carry out the plastic collapse analysis of pipelines with part-through slot under internal pressure,bending moment and axial force.The effects of various shapes and sizes of part-through slots on the collapse loads of pipelines are systematically investigated and evaluated.Some typical failure modes corresponding to different configurations of slots and loading forms are studied.

Limit Load Solution for Electron Beam Welded Joints with Single Edge Weld Center Crack in Tension

Limit loads are widely studied and several limit load solutions are proposed to some typical geometry of weldments.However,there are no limit load solutions exist for the single edge crack weldments in tension（SEC（T））,which is also a typical geometry in fracture analysis.The mis-matching limit load for thick plate with SEC（T） are investigated and the special limit load solutions are proposed based on the available mis-matching limit load solutions and systematic finite element analyses.The real weld configurations are simplified as a strip,and different weld strength mis-matching ratio M,crack depth/width ratio a/W and weld width 2H are in consideration.As a result,it is found that there exists excellent agreement between the limit load solutions and the FE results for almost all the mis-matching ration M,a/W and ligament-to-weld width ratio（W-a）/H.Moreover,useful recommendations are given for evaluating the limit loads of the EBW structure with SEC（T）.For the EBW joints with SEC（T）,the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal,when M changing from 1.6 to 0.6.When M decreasing to 0.4,the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal only for large value of（W-a）/H.The recommendations may be useful for evaluating the limit loads of the EBW structures with SEC（T）.The engineering simplifications are given for assessing the limit loads of electron beam welded structure with SEC（T）.

FRACTURE LIMIT LOAD OF CONE SHAPE PART IN DRAWING PROCESS

The deformation characters and load status of the blank＇s potential fracture zone are analyzed at the moment when blank is approaching to punch comer in drawing process of cone shape part. Based on tension instability theory, the formula for calculating fracture limit load of cone shape part in drawing process is derived. Also, the formula is analyzed and verified by experiment.

An Adaptive Load Stepping Algorithm for Path-Dependent Problems Based on Estimated Convergence Rates

A new adaptive(automatic)time stepping algorithm,called RCA(Rate of Convergence Algorithm)is presented.The new algorithm was applied in nonlinear finite element analysis of path-dependent problems.The step size is adjusted by monitoring the estimated convergence rate of the nonlinear iterative process.The RCA algorithm is relatively simple to implement,robust and its performance is comparable to,and in some cases better than,the automatic load incrementaion algorithm existent in commercial codes.Discussions about the convergence rate of nonlinear iterative processes,an estimation of the rate and a study of the parameters of the RCA algorithm are presented.To show the capacity of the algorithm to adjust the increment size,detailed discussions based on results for different limit load analyses are presented.The results obtained by RCA algorithm are compared with those by ABAQUS?,one of the most powerful nonlinear FEA(Finite Element Analysis)commercial software,in order to verify the capability of RCA algorithm to adjust the increment size along nonlinear analyses.

Limit Load Analysis of Pipes with Local Wall-thinning

The loss of metal in a pipe due to corrosion usually results in localized thinned areas with various depths and an irregular shape on its surface. In this paper, a number of numerical models of pipes with different size defects are established. The limit loads of these pipes are researched using the nonlinear finite element method. The effect of defect parameters of the local wall-thinning pipes on the limit load is discussed. The results show that limit loads decrease obviously when the depths and lengths of the defect increase. However, when the defect length reaches a certain value, the effect of defect length on limit loads is not significant. These results are compared with the results of the method of API 579. When the defect length is adequately small, the results of FEM are in good agreement with the ones of APl 579, but when the defect depth and length is adequately large, the API 579 is not suitable.

An Analysis on Limit Load for Corroded Submarine Pipelines

By means of elastic-plastic finite element analysis, a systematic nonlinear analysis of material and geometry has been carried out for submarine pipelines. A criterion for deriving limit load is studied. Based on this criterion, the limit load for corroded submarine pipelines is calculated. The corrosion length, corrosion depth and corrosion width affect the limit load. A solution to limit load is proposed and proved valid through comparison of the solution with burst test results and ASME B31G solutions.

Failure mechanism and stability control of a large section of very soft roadway surrounding rock shear slip

The measured data and simulation test phenomenon of surrounding rock deformation and failure at the project site indicate that shear failure which firstly occurs in surrounding rock, block slip and second shear failure are the root cause of deformation and damage of supporting structure of the surrounding rock at a large scale. We derived limit load of surrounding rock shear slip failure and reasonable support resistance of given load by means of shear slip line field theory, discussed the main factors which influence the limit load of surrounding rock. Shear slip line field and limit load of circular tunnel surrounding rock were obtained by means of physical simulation test, which agreed well with the theoretical analysis results. Based on the theoretical analysis and physical simulation test, the cause deformation and failure at large scale of Xinshanghai No. 1 coal mine big section ingate was analyzed, and the shear failure resistance and block slip in surrounding rock were proposed as the core technical supporting ideas. Proper range of supporting resistance which came from calculation was suggested. The support scheme which is mainly composed of large grouting anchor, sprayed anchor net support technique and full-face grille concrete finally ended the dilemma of repeated failure and mending of ingate and created critical conditions for smooth production in the coal mine.

General Analytical Shakedown Solution for Structures with Kinematic Hardening Materials

The effect of kinematic hardening behavior on the shakedown behaviors of structure has been investigated by performing shakedown analysis for some specific problems. The results obtained only show that the shakedown limit loads of structures with kinematic hardening model are larger than or equal to those with perfectly plastic model of the same initial yield stress. To further investigate the rules governing the different shakedown behaviors of kinematic hardening structures, the extended shakedown theorem for limited kinematic hardening is applied, the shakedown condition is then proposed, and a general analytical solution for the structural shakedown limit load is thus derived. The analytical shakedown limit loads for fully reversed cyclic loading and non-fully reversed cyclic loading are then given based on the general solution. The resulting analytical solution is applied to some specific problems： a hollow specimen subjected to tension and torsion, a flanged pipe subjected to pressure and axial force and a square plate with small central hole subjected to biaxial tension. The results obtained are compared with those in literatures, they are consistent with each other. Based on the resulting general analytical solution, rules governing the general effects of kinematic hardening behavior on the shakedown behavior of structure are clearly.

Weibull Statistics Strength Investigation of Synthetic Link Chains Made from Ultra-Strong Polyethylene Fibers

Chains are typically used for tension load transfer. They are very flexible and allow easy length adjustment by hooking at the links. Steel is the traditional material for chains. Recently, synthetic link chains made from ultra-strong polyethylene fibers, branded as Dyneema®, are commercially available. These chains offer a highly improved strength to weight ratio. So far, one type of such chains is available, and it has a Working Load Limit of 100 kN. 50 of such chains, containing 6 links were tested to fracture. The strength of each chain and the location of the failed link were documented during testing for later interpretation. Weibull statistics was applied in order to extrapolate towards the allowable load for very low failure risks (high reliability). Two approaches were used. One extrapolation was based on all results;the other was applied after recognition that the end links failed under a slight negative influence by the connection to the testing equipment. Thus, in fact two populations are mixed, the chains with failing end links and the chains with failing central links. So considering the population without the failing end links is more representative for pure chain behavior without clamping effects. The results from this latter consideration showed a higher Weibull exponent, thus a more realistic extrapolation behavior. Both methods indicate that the reliability at the working load limit of 100 kN is very good.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

Stability Analysis of a Multi-holes Shell Under Axial Compression

The paper presents a multi-holes shell with one hundred and eighty circular holes which has been used in engineering. Using a buckling module of the finite element analysis software, stability behavior and destroy mode along geometry parameters are studied. Results show the destroy mode depends on the geometry parameter greatly. Curves of buckling critical load and strength limited load along geometry parameters have a point of intersection. The point implies the multi-holes shell has different destroy mode and the value of point is change in geometry parameters.

Plastic limit load analysis for pressure pipe with incomplete welding defects based on the extended Net Section Collapse Criteria

With von Mises yield criterion,the loading range of Net Section Collapse(NSC) Criteria is extended from combined tension and bending loadings to combined bending,torsion and internal pressure loadings.A new theoretical analyzing method of plastic limit load for pressure pipe with incomplete welding defects based on the extended NSC Criteria is presented and the correlative formulas are deduced,the influences of pipe curvature,circumferential length and depth of incomplete welding defects on the plastic limit load of pressure pipe are considered as well in this method.Meanwhile,according to the orthogonal experimental design method,the plastic limit loads are calculated by the finite element method and compared with the theoretical values.The results show that the expressions of plastic limit load of pressure pipe with incomplete welding defects under bending,torsion and internal pressure based on extended NSC criteria are reliable.The study provides an important theoretical basis for the establishment of safety assessment measure towards pressure pipe with incomplete welding defects.

Using tandem blades to break loading limit of highly loaded axial compressors

It is confirmed that tandem-blade configurations have potential to enlarge the flow turning in two-dimension(2D) studies. However, the potential of tandem blades to enlarge the design space for highly loaded axial compressors was rarely investigated in open literatures. The present work aims to show the capability of tandem blades to break the loading limit of conventional blades for highly loaded compressors. The 2D models of the maximum static pressure rise derived in previous work were validated by a large amount experimental data, which showed a good agreement. An E parameter was defined to evaluate the stall margin of compressor based on the theoretical models, which indicated that the tandem blade was able to increase the loading limit of axial compressors. A single-blade stage with a loading coefficient of 0.46(based on the blade tip rotating speed) was designed as the baseline case under the guidance of the E parameter. A tandem-blade stage was then designed by ensuring that the velocity triangles were similar to the single-blade stage. The performances of both stages were investigated experimentally. The results showed that the maximum efficiency of the tandem-blade stage was 92.8%, 1% higher than the single;the stall margin increased from 16.9% to 22.3%. Besides, the maximum pressure rise of tandem rotors was beyond the loading limit of 2D single-blade cascades, which confirmed the potential of tandem blades to break the loading limit of axial compressors.

Improving the process forming limit considering forming defects in the transitional region in local loading forming of Ti-alloy rib-web components

The isothermal local loading forming technology provides a feasible way to form Ti-alloy large-scale rib-web components in aerospace and aviation fields.However,the local loading process forming limit is restricted by forming defects in the transitional region.In this work,the feasibility of controlling forming defects and improving the process forming limit by adjusting die parameters is explored through finite element（FE） simulation.It is found that the common cavum and folding defects in the transitional region are significantly influenced by the fillet radii of left rib and middle rib,respectively.The cavum and folding defects can be effectively controlled by increasing the fillet radii of left rib and middle rib,respectively.The process forming limits considering forming defects in the transitional region are determined by the stepwise searching method under various die parameters.Moreover,the relationship between the process forming limit and die parameters is developed through the response surface methodology（RSM）.The developed RSM models suggest that increasing the fillet radii of left and middle ribs is effective to improve the process forming limit during local loading forming of rib-web components.The results will provide technical basis for the design of die parameters and the reduction amount,which is of great importance to control forming defects and improve the process forming limit in local loading forming of Ti-alloy large-scale rib-web components.

Elasto-Plastic Test of Q235 Steel Bending Beam With Cracking Resistance

More than 30 bending beams with rectangular cross-section and different thicknesses and heights were pre- pared from Q295 steel. The specimen dimensions were about 240 mm （length） × 60 mm （height） ×70 mm （thick ness）. Flaws were cut along its middle line with a wire cutter, with lengths ranging from 6 to 35 mm. Each specimen was tested with three-point bend loading, and a process curve was obtained between load and the displacement of the loading point, in order to analyze the fracture process when opening the crack. A deformation near the prefabricated crack was observed in the testing period, and the variation of the fracture characteristic parameters was analyzed for different sizes. For a comprehensive understanding of carbon steel fracture resistance behavior, its elasticity and plas- ticity were established by determining its Young＇s modulus and Poisson＇s ratio with an optical strain gauge. This gauge was also used for the loading process test. It was found that the fracture toughness varied with the dimensions, and the toughness of the elastic limit loading was almost constant. Using the relationship of crack resistance stress intensity factor and fracture criterion, the bearing capacity of the material structure could be estimated, which shows a good agreement with the experimental test data.

The convexity about ultimate bearing hypersurfaces o structures

The relationship between the convexity on the ultimate bearing surface of a structure and the second- order effects of loads is discussed. All of generalized non-overload forces acted on a structure forms a convex set when ignoring the second-order effects （coupling effects between the generalized forces）. It is true also when the Hessian matrix composed of the second-order partial derivatives on the hypersurface about the ultimate bearing of the structure is negative definite. The outward convexity is kept when the surface is expressed by certain dimensionless parameters. A series of properties based on the convexity are pointed out. Some applications in the analysis of bearing capacity of structures were illustrated with examples. The study shows that an evaluation about the bearing capacity state of a complex structure can be made on the basis of several points on the surface of the ultimate bearing of the structure.