Limit State Design Research Articles

Evaluation of the available design models for the analysis of geosynthetic-reinforced working platforms

The working platforms for heavy construction machines demand a reliable, safe and economical ultimate limit state design procedure which enables a complete verification of safety against different failure modes. Despite considerable advances in the analysis of geogrid-reinforced working platforms through the contribution of several research studies, their proof of the stability against some crucial failure modes is still neglected in the current engineering practice. In fact, there is no universal method for the design procedure and the application of current methods and models leads to dissimilar outcomes. In this study, a comprehensive review and analysis of the current knowledge and models is performed for design of working platforms subject to the high localized forces. Accordingly, a comparative analysis is conducted to evaluate the current design models and identify the weaknesses and strengths of each prediction model.

Influence of spatial variability of soil strength on load and resistance factors calibration for the design of breakwater foundation

Many studies have recognized that spatial variability of soil (SVS) has significant influences on the reliability analysis of geotechnical engineering problems. However, the influence of SVS on the load and resistance factors (LRFs) calibrated for the limit state design of breakwater foundations has received limited attention and has become questionable. This study aims to investigate the effects of SVS on the LRFs calibrated based on a probabilistic approach. Accordingly, two breakwater foundations of the tanφ and c-tanφ forms with various scales of fluctuation and coefficients of variation of soil strength were considered. The results reveal that the SVS significantly reduces the variance of resistance and increases the positive correlation between load and resistance. These important effects of SVS strongly influence the load and resistance factors calibrated. Ignoring the SVS results in lower values of normalized resistance factor and thus a more conservative design for breakwater foundation stability outcomes. Specifically, considering SVS increases the normalized resistance factor by approximately 7%–23% for the commonly reported values of the scale of fluctuation and the coefficients of variation of soil strength. Thus, the SVS should be considered in the LRFs calibration to provide a more rational and economical design of breakwater foundations.

Reliability Analysis of Concrete Beam with High-Strength Steel Reinforcement.

In concrete structures, replacing conventional steel bars with high-strength steel reinforcement (HSSR) can effectively save the use of materials. However, the deformation properties and strength dispersion of HSSR are different from those of conventional steel reinforcement, which restricts or conservatively uses them in practical applications. For example, the partial safety factor of HRB500 grade steel bars (the yield strength is 500 MPa) in guideline GB50010-2010 is larger than that of conventional steel bars, and there is no relevant guidance for HRB600 grade steel bars (the yield strength is 600 MPa). Based on this, this paper will propose the limit state design method of high-strength steel reinforced concrete beam (HSSRCB) based on reliability analysis, which is convenient for the popularization and use of HSSR. Firstly, the flexural performance test of HSSRCBs was introduced, and the flexural capacity of HSSRCB was analyzed based on the existing prediction model. Second, a sectional numerical analysis model was established, where the section was discretized into several points, and then the curvature was gradually increased to obtain the corresponding bending moment through integration. A large number of samples were calculated to obtain statistical characteristics of the error of prediction model. Then, the limit state functions were established for two kinds of format, including partial safety factor format (PSSF) and resistance reduction factor format (RRFF), respectively, and the reliability of HSSRCBs was analyzed based on Monte Carlo simulation. Finally, the recommended values of partial safety factor of material and reduction factor of bearing capacity were proposed, in which the design strength of HRB500 and HRB600 reinforcement was 454 MPa and 545 MPa for PSSF, respectively, and the resistance reduction factor for the flexural capacity of HSSRCB was 0.8 and 0.75 for RRFF, respectively.

Contribution of the standard penetration test SPT to the design of pile foundations in sand– Practical recommendations

The objective of this article is to present original research work results on the contribution of the standard penetration test (SPT) to the design and analysis of pile foundations on the basis of the interpretation of a database of full-scale pile loading tests undertaken in sandy soils, with the aim to provide practical recommendations to the designers. The article encompasses three parts, the first one presents a detailed comparative study of 10 currently used methods of design on the basis of the SPT, assessed according to their predictive capability of the axial bearing capacity, within a database consisting of 46 axial pile loading tests carried out in 27 sites in the United Arab Emirates. The second part presents some experimental findings related to the critical (or creep) vertical load, whereas the third part highlights the concept of the reference pile settlement and its application to the limit state design of pile foundations.

Combined Gaussian Local Search and Enhanced Comprehensive Learning PSO Algorithm for Size and Shape Optimization of Truss Structures

This paper proposes the use of enhanced comprehensive learning particle swarm optimization (ECLPSO), combined with a Gaussian local search (GLS) technique, for the simultaneous optimal size and shape design of truss structures under applied forces and design constraints. The ECLPSO approach presents two novel enhancing techniques, namely perturbation-based exploitation and adaptive learning probability, in addition to its distinctive diversity of particles. This prevents the premature convergence of local optimal solutions. In essence, the perturbation enables the robust exploitation in the updating velocity of particles, whilst the learning probabilities are dynamically adjusted by ranking information on the personal best particles. Based on the results given by ECLPSO, the GLS technique takes data from the global best particle and personal best particles in the last iteration to generate samples from a Gaussian distribution to improve convergence precision. A combination of these techniques results in the fast convergence and likelihood to obtain the optimal solution. Applications of the combined GLS-ECLPSO method are illustrated through several successfully solved truss examples in two- and three-dimensional spaces. The robustness and accuracy of the proposed scheme are illustrated through comparisons with available benchmarks processed by other meta-heuristic algorithms. All examples show simultaneous optimal size and shape distributions of truss structures complying with limit state design specifications.

Residual ultimate strength assessment of submarine pressure hull under dynamic ship collision

This study aims to develop numerical simulations and empirical equations to predict the ultimate residual strength of dented submarine pressure hulls. The collision scenarios considered in this study include accidents between submarine pressure hulls and attendant vessels or floating objects. First, numerical approaches were developed for dynamic collision and collapse simulations. The accuracy of the developed numerical method was validated by comparing its results with existing test results. Then, the parametric studies were conducted with a series of numerical simulations on the actual submarine pressure hull dimensions with various collision loading scenarios using ABAQUS v6.14 tools. Finally, empirical equations were established using the results from Nonlinear Finite Element Analysis (NFEA) database. The reliability of the derived equations was assessed by comparing their results with the NFEA results and the available test data. These equations are simple to use for the initial design and serviceability limit state of submarine pressure hulls subjected to collision accidents in real cases.

Calibration of Temperature Gradient Load Factor for Service Limit State Design of Concrete Slab-on-Girder Bridges

Calibration of Temperature Gradient Load Factor for Service Limit State Design of Concrete Slab-on-Girder Bridges

Gaussian mixture model for extreme wind turbulence estimation

Abstract. Uncertainty quantification is necessary in wind turbine design due to the random nature of the environmental inputs, through which the uncertainty of structural loads and response under specific situations can be quantified. Specifically, wind turbulence (described by the standard deviation of the longitudinal wind speed over a 10 min time duration) has a significant impact on the extreme and fatigue design envelope of the wind turbine. The wind parameters (mean and standard deviation of longitudinal wind speed over 10 min time duration) are not independent stochastic variables, and structural reliability analysis or uncertainty quantification therefore requires these wind parameters to be correlated stochastic parameters. An accurate probabilistic model should be established to model the correlation among wind parameters. Compared to univariate distributions, theoretical multivariate distributions are limited and not flexible enough to model the wind parameters from different sites or direction sectors. Copula-based models are often used for correlation description, but existing parametric copulas may not model the correlation among wind parameters well, due to limitations of the copula structures. The Gaussian mixture model is widely applied for density estimation and clustering in many domains, but limited studies have been conducted in wind energy and few have used it for density estimation of wind parameters. In this paper, the Gaussian mixture model is used to model the joint distribution of mean and standard deviation of longitudinal wind speed over 10 min time duration, which is calculated from 15 years of wind measurement time series data. As a comparison, the Nataf transformation (Gaussian copula) and Gumbel copula are compared with the Gaussian mixture model in terms of the estimated marginal distributions and conditional distributions. The Gaussian mixture model is then adopted to estimate the extreme wind turbulence (wind parameters for extreme load), which could be taken as an input to design loads used in the ultimate design limit state of turbine structures. The wind parameter contour associated with a 50-year return period computed from the Gaussian mixture model is compared with what is used in the design of wind turbines as given in IEC 61400-1. The Gaussian mixture model is able to model the joint distribution of wind parameters well, where the estimated tail distributions of both the marginal distributions and conditional distribution have good accuracy, and it is a good candidate for extreme turbulence estimation.

Experimental Study on External Loading Performance of Large Diameter Prestressed Concrete Cylinder Pipe

A prestressed concrete cylinder pipe (PCCP) is created with a complex composition of concrete core, welded steel cylinder, prestressed steel wire, protective mortar and anti-corrosion coating. Due to the economy and complexity of structural prototype tests, the ultimate loading test on PCCP is rarely conducted. In this paper, the three-edge bearing test was carried out on a 3.2 m diameter PCCP with embedded steel cylinder. The strains of concrete core, prestressed steel wire and protective mortar were monitored, and the distribution and width of the concrete cracks were recorded. The test results show that the cracking on the inside concrete at the crown zone occurred before those on the invert zone of the pipe. The prestressed steel wire postponed the tensile stress of out-side concrete at the springing line until subjected to the calculated cracking load (Pc). Due to the moment redistribution caused by the cracking on the inside of the concrete at the crown/invert, the protective mortar at the springing line was cracked at 1.2 Pc and exhibited visible cracking after 1.4 Pc. The prestressed steel wire reached the elastic and strength limit states of 1.4 Pc and 1.6 Pc, respectively. The PCCP designed by the limit state design method can resist the increased external loads after reaching the serviceability limit state. The final failure load of the test pipe is greater than 1.6 Pc, and there is sufficient safety in actual operation. Due to the fact that the damage to the concrete at the crown/invert zone may become a fuse of PCCP failure, the tensile stress of the inside concrete at the crown/invert zone of the PCCP should be accurately verified in the design process.

Machine Learning Based Design of Railway Prestressed Concrete Sleepers

The state-of-the-art design methods for railway prestressed concrete sleepers are currently based on the quasi-static stresses resulting from a simplification of dynamic wheel loads, and subsequently the quasi-static responses of concrete sleepers. This method has been widely used in practices to overcome the complexity of dynamic analysis and testing. A single load factor (or called dynamic impact factor) for a partial safety-factored design (or k factors for the test criteria) is commonly used to crudely account for dynamic train–track interactions over different levels of track irregularities. The dynamic impact factors for either design or testing are usually obtained from either (i) railway infrastructure managers (i.e., in EN 13230), or (ii) prescribed standardised factors (i.e., AS 1085.14, AREMA Chapter 30, JSA—JIS E 1201). The existing design concepts for prestressed concrete sleepers using either (i) an allowable stress design or (ii) the limit state design method require many iterations for calculations and optimisations. The design process to achieve optimal products suitable for track, operational, and environmental parameters is, thus, very time-consuming. On this ground, this study investigates the potential capability of machine learning (ML) to learn from large amounts of design data sets and then to facilitate the design and capacity prediction of railway prestressed concrete sleepers. Three ML algorithms are developed, namely deep learning, Bayesian Neural Network, and random forest. Through a combination of hand-calculated design data, industry design data, and experimental investigations in compliance with EN 13230, over 3000 sets of design data have been collected. These data sets are used to assimilate a comprehensive database for machine learning. Four indicators, namely mean squared error (MSE), root-mean-square error (RMSE), mean absolute error (MAE), and R2 are used to benchmark the accuracy and precision of machine learning models. Our results reveal that the random forest algorithm offers the best performance. The values of MSE, RMSE, MAE, and R2 are 0.54, 0.74, 0.25, and 0.99, respectively. Note that the Bayesian neural network also performs very well. In contrast, the deep learning algorithm performs worse than the others. The insight demonstrates machine learning’s capability to aid in the design of railway prestressed concrete sleepers, to satisfy both serviceability and ultimate limit states

Electrochemical/Microstructural Studies on the Corrosion of Prestressed Steel Strand in Concrete with Naturally Ingressing Chlorides

The occurrence of environmentally assisted cracking (EAC) is as dependent on the aggressiveness of the environment as the susceptibility of the material and the presence of static tensile stresses. However, the influence of the environment has not been adequately considered in past investigations on EAC mechanisms of prestressing strands. This study utilizes various characterization techniques to evaluate the surface/bulk deterioration of corroded pretensioned concrete (PTC) specimens after natural chloride exposure (by diffusion through cover concrete). Corroded strands in two PTC prism specimens (3,000 mm × 150 mm × 200 mm) were characterized using electrochemical impedance spectroscopy (EIS) and other microanalytical techniques. The EIS and scanning electron microscope (SEM) images obtained after 1 y and 2 y of exposure revealed a negligible residual protectiveness of the passivated surface (although the concretes possessed high resistivity). Raman spectra, SEM, and x-ray computed tomography images of extracted corroded strands also provided unique insights into the pattern of corrosion propagation in PTC systems subjected to realistic chloride exposure. Microcracks in the bulk metal beneath flat-bottomed corrosion pits revealed the possible EAC at low chloride levels expected in service (<0.6% by weight of binder). The findings serve as a basis to define chloride-induced passive-to-active transition as the end of risk-free service life of PTC structures, and for considering it as the limit state for both service life design and corrosion assessment to avoid the onset of EAC.

Application of Eurocode 7 for the analysis and design of veneer cover soils in static and seismic load conditions

Veneer is intended as a relatively thin cover soil layer placed on a slope. Veneer cover soil systems in containment facilities such as landfills, liquid disposal and reservoirs involve geosynthetic-soil interfaces. The main design criterion for protective veneer covers is to ensure that no sliding occurs above the geosynthetic or the existing soil slope. The design of the protective veneer covers should include the stability of the lining system under the effect of the gravity forces, equipment loadings, seismic actions and pore water pressures. The limit equilibrium method used in the present paper for the evaluation of veneer stability has been derived from the method of Koerner and Soong (1988) and adapted to the limit state design offered by Eurocode 7 with reference to the Resistance Factor Approach (RFA). Serviceability limit state considerations are included in the design method for completeness.

Analyzing the influence of facing batter on reinforcement loads of reinforced soil walls under working stress conditions

The level of reinforcement loads in a reinforced soil retaining wall is important to its satisfactory operation under working stress conditions since it basically determines the wall deformation. Consequently, proper estimation of the reinforcement load is a necessary step in the service limit-state design of this type of earth retaining structures. In this study, a force equilibrium approach is proposed to quantify the influence of facing batter on the reinforcement loads of reinforced soil walls under working stress conditions. The approach is then combined with a nonlinear elastic approach for GRS walls without batter to estimate the reinforcement loads neglecting toe restraint. The approximate average mobilized soil strength in the retaining wall is employed in the force equilibrium analysis. The predictions of reinforcement loads by the proposed method were compared to the experimental results from four large-scale tests. It is shown that the proposed semianalytical approach has the capacity to reproduce the reinforcement loads with acceptable accuracy. Some remaining issues are also pinpointed.

The Design of Concrete Beams Reinforced with GFRP Bars Based on Crack Width.

Since glass fiber-reinforced polymer (GFRP) bars have a lower modulus than steel bars, the design of GFRP-reinforced concrete (GFRP-RC) is often governed by the serviceability limit state (deflection and cracking) rather than the ultimate state. A new design method has been proposed in this paper for GFRP-RC beams based on the flexure crack width. The state when the maximum flexure crack width in the tensile zone reaches the limit of 0.5 mm specified by ACI 440.1R-15 was used as the design limit state. The concrete compressive strain at the extreme compression fiber of concrete under the design limit state was obtained by four-point bending tests of eight full-scale GFRP-RC beams and finite element analysis. Based on the concrete compressive strain under the design limit state and cross-sectional analysis, a design method for calculating the longitudinal reinforcement ratio of GFRP-RC beams under the design limit state is proposed. This design method is proven to be feasible by the experimental and the finite element results. In addition, the flexural capacity coefficient was discussed to investigate the safety reserve of the design method.

Feasibility study of flopper stoppers as a passive roll compensation system for offshore construction vessels

Heavy lift vessels are used to install offshore infrastructure. For floating vessels, roll responses can significantly limit their operability, especially for offshore sites where multimodal wave spectra are expected. This paper deals with a numerical study of a heavy lift vessel equipped with submerged flopper stopper (FS) templates suspended from the sides of the vessel. Dynamic analyses for various sizes and numbers of FS templates were conducted. A medium-size (28 m × 14 m) template can increase operational limits by shifting the roll’s natural frequency towards lower values and dampening the responses through drag forces. The operability can increase by about 500% when compared with a vessel without FS templates. A preliminary structural design of a critical beam shows an ultimate limit state design safety factor of 1.5 and fatigue damage of 0.32 for 20 years of service. The cost of construction per template is about $1.75 million (U.S. dollars); the total cost of 4 templates could be recovered in a single wind farm installation project. The system is shown to be feasible for construction vessels used in the execution of marine operations, especially heavy lifting.

Direct Design of Stainless Steel Frames: Recommendations and Case Studies

AbstractAcknowledging the potential of system‐based design approaches, most international design standards for steel structures include preliminary versions of such alternative design methods. The Direct Design Method (DDM) is one of these approaches, which allows designing steel structures directly using advanced numerical analyses without requiring further member checks. This paper presents the DDM design (and verification) procedure and summarizes the key aspects of the advanced finite element model necessary for the determination of the system strength, with an emphasis on cold‐formed stainless steel portal frames. Through the design of two frames, the DDM design procedure is illustrated and the resulting cross‐sections are compared with those derived using the traditional two‐step design approach in the Eurocode and ASCE design frameworks. The results demonstrate that the DDM verification process is simpler and more direct, and that lighter structures are obtained when designing using the DDM for strength considerations. Finally, this paper also highlights that allowing larger deformations in the ultimate limit state design for the DDM does not have additional negative effects on the serviceability requirements if compared to the traditional two‐step design approach.

Gradient-based optimisation of rectangular honeycomb core sandwich panels

When subjected to bending loads, sandwich panels are highly efficient structural components with the potential to achieve substantial weight reduction. A successful design methodology for sandwich panels should aim at maximising this potential for weight reduction while considering the various possible failure mode in a simple yet accurate manner. This paper investigates the application of steel sandwich panels as two-way deck systems. Near-optimal designs for all-steel Rectangular Honeycomb Core Sandwich Panels (RHCSPs) under general out-of-plane loading are achieved using a gradient-based optimisation method. The method relies on continuously optimising the design limit state constraints while the response constraints are considered a priori in the analysis stage using simplified analytical assessment. Plate bending solutions and sandwich bending solutions are used as alternatives to estimate the internal stresses on each layer of the sandwich panel under out-of-plane loads, where comparisons are made between these two analysis methods in terms of computational efficiency and accuracy. The internal stresses are then used to formulate design limit state equations for each relevant failure mode, including material yielding, plate buckling and deformation control. The Method of Moving Asymptotes is used for the optimisation of RHCSPs, considering the limit states as the constraints of the optimisation problem and weight as the objective function to be minimised. The proposed methodology for simplified assessment is verified against detailed nonlinear finite element models for optimal design solutions. The implications of the results of the proposed optimisation strategy on the development of a systematic design methodology for RHCSPs are also highlighted, making specific reference to critical failure modes.

Deflection analysis of welded steel I‐girders with corrugated webs based on first yield

AbstractSinusoidal corrugated profile webs have been popularly used in steel structural designs to replace the flat webs in conventional welded beams, while there are better performances in corrugated web beams (CWBs) regarding more stability and less material used to against beam failures caused by buckling. Previous studies have provided that CWBs enabled numerous favourable benefits to be recognised as alternatives to the traditional weld beams in designing structures. Furthermore, as CWBs are proposed as the major load‐carrying elements, the maximum deflection in the elastic range is one of the important beam properties that should be precisely estimated and calculated. To find an appropriate method in computing the maximum deflection of CWBs based on the first yield for civil communities in Australia, proposed equations based on other standards will be employed to calculate the theoretical results for the comparisons with simulation‐based results. While applying the linear analysis simulations provided by SAP 2000, ultimate limit state design theory has also been used with requirements stated by AS 4100. In this study, the results in theoretical calculations and numerical simulations have been compared to conclude that the highly defined equations by ASTM [37] and Sause et al. [38] could precisely estimate the maximum deflections of CWBs based on the first yield in conjunction with requirements and limitations in Australian standards, which could be adequate for the structural design calculations in Australian design fields.

Failure experiment and calculation model for prestressed concrete cylinder pipe under three-edge bearing test using distributed fiber optic sensors

A prestressed concrete cylinder pipe (PCCP) with quality defects or being subjected to overloads can crack in the inner concrete core, thereby the internal water acting directly on the steel cylinder and further weakening the bearing capacity of the pipe. This study aims to explore calculation methods of when and after a PCCP cracks through the comparative analysis between the test results measured from the three-edge bearing test (TEBT) and the calculation results through the improved procedures based on ANSI/AWWA C304. To this end, the full strain distribution around the circumference of the first pipe is measured until failure by distributed optical fiber sensors. The thrust and moment coefficients of loads under the TEBT are derived, and strains are solved considering the stress–strain relationships of the constituent materials. The first pipe cracks in the inner core at the crown and invert as the load reaches 280 kN/m, but the second pipe with the same parameters does not crack when the load arrives at 360 kN/m. The measured strains reveal that the inner side at the crown and invert and the outer side at the springline are subjected to tension. Before appearing the cracks in the inner concrete core, the calculated results are in good agreement with experimentally observed data. After cracking of the inner concrete core, both the vertical displacement at the crown and the fluctuation amplitude of test strains begin to accelerate. The results calculated by considering two empirical assumptions can reflect the trend of the test results. The proposed comparative analysis approach provides the cracking test load that meets the serviceability limit-state design criterion for quality inspection and helps designers a better understanding of design assumptions and parameters.

Reliability of stainless steel frames designed using the Direct Design Method in serviceability limit states

Steel structures can be consistently and efficiently designed using system-based design-by-analysis approaches such as the Direct Design Method. However, since direct design approaches lead to potentially lighter structural configurations, they can also result in larger deformations under service loads. Thus, greater attention may be required to serviceability limit states in structures designed using design-by-analysis approaches than for structures designed elastically at their ultimate limit state following current two-stage approaches, especially for materials showing highly nonlinear stress vs strain responses such as stainless steel alloys. With the aim of investigating the influence of allowing larger deformations in the ultimate limit state design of stainless steel structures, this paper presents an explicit analysis framework for assessing serviceability reliability at system level. Using this framework, the paper investigates the serviceability reliability of cold-formed stainless steel portal frames designed using the Direct Design Method for different load cases, including the gravity load and the combined gravity plus wind load combinations. The study considers six baseline frames covering the most common stainless steel families and international design frameworks (i.e., Eurocode, US and Australian frameworks), for which the reliability of vertical deflection and lateral drift serviceability limit states is investigated using advanced numerical simulations and First-Order Reliability Methods. From the comparison of the calculated average annual reliability indices and the relevant target reliabilities for the different design frameworks, it was found that the reliability of stainless steel frames appears to be adequate for the serviceability limit states investigated for the Eurocode, US and Australian frameworks.