Calibration of LRFD Format for Steel Jacket OffshorePlatform in China Offshore Area(2): Load, Resistance and Load Combination Factors

Adopting the load and resistance factor design format, the design method for steel jaeket platform structures is developed. Firstly, the limit state equations and design format for steel jacket platform structures are introduced. Then, the ratio of live load effect to dead load effect is estimated. The target reliabilities for design of offshore structures in China offshore area are calibrated by past practice in API RP2A-WSD code. The load and resistance factors are optimized by minimizing the difference within the target reliability and the resulting reliability over the range of load effect ratios. Considering the concurrence of different loads, load combination factors are obtained through an optimization process, and the relation between the load combination factor and load correlation coefficient is established. Finally, the design formulae for steel jacket structures in China offshore area are recommended.

Inferring rules for adverse load combinations to crack in concrete dam from monitoring data using adaptive neuro-fuzzy inference system

The formation and growth of cracks in concrete dams are mainly induced by hydrostatic and temperature loads.As cracks es-pecially unstable cracks are of great danger to the safety of dams,it is critical to avoid extremely adverse load combinations during the dam operations to achieve the stability of cracks.Conventionally,the adverse load combinations have to be deter-mined empirically by experts based on specific dam site conditions.Therefore,it is attractive to apply quantitative instead of empirical methods to identify the adverse loading conditions.In this study,we employ an adaptive neuro-fuzzy inference sys-tem(ANFIS) to Chencun concrete dam.The ANFIS is able to help us build a relationship between the model inputs(reservoir water level and air temperature) and the model output(crack opening displacement).Based on this relationship,the rules of the adverse load combinations to the crack are generated directly from the monitoring data.The accuracy of the trained ANFIS is proved by comparing the modeling results and the monitoring data.Our work demonstrates that the ANFIS is a useful ap-proach for accurately recognizing the rules of the adverse load combinations that can be used in the knowledge base of dam safety expert system.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures(AS)within deep roadways can result in cumulative damage and failure.This study develops an experimental device designed to test AS under triaxial loads.The device enables the investigation of the mechanical response,failure mode,instability assessment criteria,and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths.The results show that the peak bearing strength is positively correlated with the anchoring matrix strength,anchorage length,and edgewise compressive strength.The bearing capacity decreases significantly when the anchorage direction is severely inclined.The free face failure modes are typically transverse cracking,concave fracturing,V-shaped slipping and detachment,and spallation detachment.Besides,when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength,loading rate,and anchorage inclination angle increase,the failure intensity rises.Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend.Under cyclic loads,the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability.Finally,a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

Similarity Criterion and Scale Effect for Ship Distortion Model Under Combined Loads

For the ultimate strength model test evaluation of large ship structures, the distortion model with non-uniform ratio between the main size and the plate thickness size is usually adopted. It is the key to carry out scale model test to establish a distortion model similar to the real ship structure under combined load. A similarity criterion for ship distortion model under the combined action of bending moment and surface pressure was proposed, and the scale effect for the criterion was verified by a se ries of numerical analysis and model tests. The results show that the similarity criterion for ship distor tion model under combined loads has a certain scale effect. For the model tests of ship cabin struc tures, it is suggested that the scale range between the plate thickness scale and the main dimension scale should be controlled within 2:1, which can be used as a reference for distortion model design and ultimate strength test of large-scale ship structures.

Reliability-Based Load and Resistance Factors Design for Offshore Jacket Platforms in the Bohai Bay:Calibration on Design Factors

For the fulfillment of the probability-based structural design for the offshore jacket platforms in the Bohai Bay, the design factors of loads, resistance and load combinations are much necessary to be calibrated according to the proposed target reliability index. Firstly, the limit states function for the offshore jacket platforms is introduced. Then, four approaches to calibrate the factors of load and resistance are presented and compared. Afterwards, the methods to calibrate the load combination factors are developed. Finally, the factors of load, resistance and load combination for the offshore jacket platforms in the Bohai Bay are calibrated and the corresponding design formulae are recommended. The results are proved to be rational in practice, and also illustrate that the proposed target reliability index for offshore jacket platforms in the Bohai Bay is also appropriate.

Reliability analysis of marine risers with narrow and long corrosion defects under combined loads

A marine riser,one of the most important components of offshore oil/gas transportation,needs to be designed to eliminate the risks caused by complex ocean environments,platform displacement and internal corrosion,etc.In this study,a new analytical-numerical assessment approach is proposed in order to quantitatively investigate the reliability of internally corroded risers under combined loads including axial tension and internal pressure.First,an analytical solution of the limit state function of intact risers under combined loads is obtained,which is further modified by the non-dimensional corrosion depth （d/ t） for the risers with a narrow and long corrosion defect.The relationship between d/t and limited internal pressure is obtained by finite element analysis and nonlinear regression.Through an advanced first-order reliability method （HL-RF） algorithm,reliability analysis is performed to obtain the failure probability,the reliability index and the sensitivity.These results are further verified by Monte-Carlo importance sampling.The proposed approach of reliability analysis provides an accurate and effective way to estimate the reliability of marine risers with narrow and long corrosion defects under combined loads.

Study on Failure Mechanism and Bearing Capacity of Three-Dimensional Rectangular Footing Subjected to Combined Loading

This paper presents two kinematic failure mechanisms of threc-dimensional rectangular footing resting on homogeneous undrained clay foundation under uniaxial vertical loading and uniaxial moment loading. The failure mechanism under vertical loading comprises a plane strain Prandti-type mechanism over the central part of the longer side, and the size of the mechanism gradually reduces at the ends of the longer side and over the shorter side as the corner of rectangular footing is being approached where the direction of soil motion remains normal to each corresponding side respectively. The failure mechanism under moment loading comprises a plane strain scoop sliding mechanism over the central part of the longer side, and the radius of scoop sliding mechanism increases linearly at the ends of the longer side. On the basis of the kinematic failure mechanisms mentioned above, the vertical ultimate bearing capacity and the ultimate bearing capacity against moment or moment ultimate bearing capacity are obtained by use of upper bound limit analysis theory. At the same time, numerical analysis results, Skempton＇ s results and Salgado et al. ＇s results are compared with this upper bound solution. It shows that the presented failure mechanisms and plastic limit analysis predictions are validated. In order to investigate the behaviors of undrained clay foundation beneath the rectangular footing subjected to the combined loadings, numerical analysis is adopted by virtue of the general-purpose FEM software ABAQUS, where the clay is assumed to obey the Mohr-Coulomb yielding criterion. The failure envelope and the ultimate bearing capacity are achieved by the numerical analysis results with the varying aspect ratios from length L to breadth B of the rectangular footing. The failure mechanisms of rectangular footing which are subjected to the combined vertical loading V and horizontal loading H （Vertical loading V and moment loading M, and horizontal loading H and moment loading M respectively are observed in the finite element analysis. ） is explained by use of the upper bound plasticity limit analysis theory. Finally, the reason of eccentricity of failure envelope in H-M loading space is given in this study, which can not be explained by use of the traditional ＇ swipe test＇.

Elastoplastic solutions for single piles under combined vertical and lateral loads

In order to improve the reliability of the design and calculation of single piles under the combined vertical and lateral loads, the solutions were presented based on the subgrade reaction method, in which the ultimate soil resistance was considered and the coefficient of subgrade reaction was assumed to be a constant. The corresponding computational program was developed using FORTRAN language. A comparison between the obtained solutions and the model test results was made to show the validity of the obtained solutions. The calculation results indicate that both the maximum lateral displacement and bending moment increase with the increase of the vertical and lateral loads and the pile length above ground, while decrease as the pile stiffness, the coefficient of subgrade reaction and the yielding displacement of soil increase. It is also shown that the pile head condition controls the pile responses and the vertical load may cause the instability problem to the pile. In general, the proposed method can be employed to calculate the pile responses independent of the magnitude of the pile deflection.

Failure Loci of Suction Caisson Foundations Under CombinedLoading Conditions

Suction caissons are widely used to support offshore fixed platforms in coastal areas. The loadings transferred to suction caissons include the eccentric lateral force induced by waves and self weight of the platform structure. However, under this kind of combined loading conditions, the failure mechanism of caissons with shallow embedment depths is quite different from conventional deep foundations or onshore shallow footings. The behaviour of caissons subjected to combined loadings may be described with the ＂failure locus＂ in force resultant spaces. Here the failure loci of smooth caissons are studied by use of finite dement approach, with the embedment ratio of caissons varying in the range of 0.25 - 1.0 and eccentricity ratio of horizontal loadiugs in 0 - 10. The platform settlement and tilt limits are involved into determination of failure loci, thus the platforms can avoid significant displacements for the combined loadings located inside the failure locus. Three families of loading paths are used to map out the locus. It is found that the shape of failure loci depends on 3 non-dimensional parameters, and the failure locus of a given caisson changes gradually from the elliptical curve to hooked curve with increasing shear strength of soil. The lateral capacity of short caissons may be enhanced by vertical forces, compared with the maximum lateral capacity of long caissons occurring at the vertical force being zero. The critical embedment ratios partitioning elliptical and hooked loci are proposed.

Undrained Bearing Capacity of Spudcan Under Combined Loading

The bearing capacities of spudcan foundation under pure vertical （/1）, horizontal （H）, moment （M） loading and the combined loading are studied based on a series of three-dimensional finite element analysis. The effects of embedment ratio and soil non-homogeneity on the bearing capacity are investigated in detail. The capacities of spudcan under different pure loading are expressed in non-dimensional bearing capacity factors, which are compared with published results. Ultimate limit states under combined loading are presented by failure envelopes, which are expressed in terms of dimensionless and normalized form in three-dimensional load space. The comparison between the presented failure envelopes and available published numerical results reveals that the size and shape of failure envelopes are dependent on the embedment ratio and the non-homogeneity of the soil.

Buckling analysis of shear deformable composite conical shells reinforced by CNTs subjected to combined loading on the two-parameter elastic foundation

The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.

Testing Studies on Rock Failure Modes of Statically Loads Under Dynamic Loading

By means of the improved split Hopkionson pressure bar(SHPB) with axial pre-pressure and confined pressure, two series of experiments on sandstone are carried out to research the failure mode of rock during the course of exploitation of resources in deep. One is under the conditions that the con-fining pressure is fixed and the axial pressure is changeable. The other is under the conditions that the confining pressure becomes and the axial pressure is fixed. It is found that samples break up evenly after impacting when axial static pressures are low, there is great disparity in size of fragments when axial static pressures are high, and the main bodies of samples after the tests under the combination of dy-namic and static loads frequently show the type of V or X. The samples are more close-grained at the elastic stage and impacts make many cracks be generated and developed, as makes samples more crackable. At the initial phase of damage stage, the static pressures make some cracks in the samples which are undeveloped and the impacts′ role is similar to that at the elastic stage. At the metaphase or anaphase of damage stage, these cracks in the samples develop adequately and the impacts mainly accelerate samples′ failure. The main bodies of samples show the type of V or X after impacting due to the confining pressures′ restraining samples′ lateral formation at the elastic stage or the initial phase of damage stage, the main bodies of samples have almost formed at the stage loading static pressures and the results after impacting usually are similar to those under the axial pressures tests.

Analytic elasticity solution of bi-modulus beams under combined loads

A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤ 5. The error also varies with the distributed load patterns.

Combined load bearing capacity of rigid piles embedded in a crossanisotropic clay deposit using 3D finite element lower bound

In this study,an iterative-based three-dimensional finite element lower bound in association with the second-order cone programming method is adopted to evaluate the limit load of a single pile embedded in cross-anisotropic soils under general loading condition.The lower bound solutions of the pile embedded in an anisotropic soil deposit can be found by formulating the element equilibrium,equilibrium of shear and normal stresses along discontinuities,boundary conditions,yield function,and optimizing the objective function through the second-order cone programming method in conjunction with an iterative-based update procedure.A general loading condition is considered to profile the expansion of the safe load in the vertical-horizontal-moment(V-H-M)space.The results of this study are compared and validated against three different cases including an isotropic lateral loading,anisotropic end bearing capacity,and a pile embedded in an isotropic soil deposit under general loading condition.A parametric study is conducted to evaluate the impact of different influencing factors.It was found that the effect of anisotropy on the variation of lateral limit load of a single pile is more pronounced than the corresponding vertical and bending moment limit loads,whereas the interface properties have more significant effects on the vertical and bending moment limit loads in comparison to the lateral limit load.

Influence of Vertical Load on Lateral-Loaded Monopiles by Numerical Simulation

Monopiles are the most common foundation form of offshore wind turbines,which bear the vertical load,lateral load and bending moment.It remains uncertain whether the applied vertical load increases the lateral deflection of the pile.This paper investigated the influence of vertical load on the behaviour of monopiles installed in the sand under combined load using three-dimensional numerical methods.The commercial software PLAXIS was used for simulations in this paper.Monopiles were modelled as a structure incorporating linear elastic material behaviour and soil was modelled using the Hardening-Soil(HS)constitutive model.The monopiles under vertical load,lateral load and combined vertical and lateral loads were respectively studied taking into account the sequence of load application and pile slenderness ratio(L/D;L and D are the length and diameter of the pile).Results suggest that the sequence of load application plays a major role in how vertical load affects the deflection behaviour of the pile.Specifically,when L/D ratios obtained by lengthening the pile while keeping its diameter constant are 3,5 and 8,the relationships between lateral load and the deflection behaviour of the pile under the effect of vertical load demonstrate a similar trend.Furthermore,the cause of increased lateral capacity of the pile under the action of applied vertical load in the common practical application case and in the VPL case was analyzed by studying the variation law of soil stress along the pile embedment.Results confirm that the confining effect of vertical load increases means effective stress of the soil around the pile,thus increasing soil stiffness and pile capacity.

Ultimate Load Capacity of Offshore Pipeline with Arbitrary Shape Corrosion Defects

A set of generalized solutions are proposed for estimating ultimate load capacity of pipeline with arbitrary corrosion shapes subjected to combined internal pressure, axial force and bending moment. Isotropic and anisotropic material characteristics in longitudinal and circumferential direction of pipeline are also considered in the proposed equations. Simplified numerical method is used to solve the generalized expressions. The comparisons of numerical results based generalized solutions and full-scale experimental results are carried out. The predicted results agree reasonably well with the experiment results. Meanwhile, the effects of corrosion shapes and locations on the ultimate load capacity are studied.

Dynamic response of UHMWPE plates under combined shock and fragment loading

Ultra-high molecular weight polyethylene(UHMWPE)fiber composite has been extensively used to construct lightweight protective structures against ballistic impacts,yet little is known about its performance when subjected to combined blast and fragment impacts.Built upon a recently developed laboratory-scale experimental technique to generate simulated combined loading through the impact of a fragment-foam composite projectile launched from a light gas gun,the dynamic responses of fullyclamped UHMWPE plates subjected to combined loading were characterized experimentally,with corresponding deformation and failure modes compared with those measured with simulated blast loading alone.Subsequently,to explore the underlying physical mechanisms,three-dimensional(3D)numerical simulations with the method of finite elements(FE)were systematically carried out.Numerical predictions compared favorably well with experimental measurements,thus validating the feasibility of the established FE model.Relative to the case of blast loading alone,combined blast and fragment loading led to larger maximum deflections of clamped UHMWPE plates.The position of the FSP in the foam sabot affected significantly the performance of a UHMWPE target,either enhancing or decreasing its ballistic resistance.When the blast loading and fragment impact arrived simultaneously at the target,its ballistic resistance was superior to that achieved when subjected to fragment impact alone,and benefited from the accelerated movement of the target due to simultaneous blast loading.

Behavior of Reinforced Concrete Columns under Combined Axial Load and Bending in Accordance with a Nonlinear Numerical Model

A nonlinear numerical model was developed to analyze reinforced concrete columns under combined axial load and bending up to failure. Results of reinforced concrete columns under eccentric compression tested to failure are presented and compared to results from a numerical nonlinear model. The tests involved 10 columns with cross-section of 250 mm × 120 mm, geometrical reinforcement ratio of 1.57% and concrete with compression strength around 40 MPa, with 3,000 mm in length. The main variable was the load eccentricity in the direction of the smaller dimension of cross-section. Experimental results of ultimate load and of the evolution of transverse displacements and concrete strains are compared with the numerical results. The estimated results obtained by the numerical model are close to the experimental ones, being suitable for use in verification of elements under combined axial load and bending.

A New Fracture Criterion for a Crack under Combined Mode Loading

A new fracture criterion was proposed. The physical explanation of the criterion is that crack will propagate when the minimum strain energy density in iso hoop stress curve reach a critical strength of the material considered. The resulting curve of critical fracture of mixed mode cracks shows that the present fracture is efficient and more accurate than the previous criteria.

LARGE DEFLECTION PROBLEM OF CIRCULAR PLATES WITH VARIABLE THICKNESS UNDER THE ACTION OF COMBINED LOADS

By using the modified iteration method of large deflection theory of plates with variable thichness[1], we solve the problem of circular plates with variable thickness subjected to combined loads under the boundary conditions of the clamped edges and get comparatively more accurate second-order approximate analytical solution. If the results of this paper are degraded into the special cases, the results coinciding with those of papers [1,2] can be obtained. In this paper, the characteristic curves are plotted and some comparisons are made. The results of this paper are satisfactory.