Oct 2026· Journal of engineering mechanics· 0 citations· 28 references
Abstract
It is generally agreed that engineered structures, whether bridges or aircraft, should be designed to have failure probability no higher than
10
−
6
per lifetime. The safety analysis of concrete structures based on the current design codes cannot guarantee meeting this goal. While sophisticated probabilistic models have been developed to deal with the randomness of loads, the uncertainty of material failure has been relegated to empirical understrength (or capacity reduction) factors. The problem is that the design equations of all design codes have traditionally been formulated as lower-margin equations, set at the lower margin of the test data cloud (which lies, depending on structure size, 25% to 40%, below the data mean, in the case of shear strength of RC beams). The load factors are applied to these lower-margin equations while the offset of the mean and the variance of the database remain buried in the code committee documents. Moreover, probabilistic modeling of the mechanics of failure processes, which determines structural strength, has been incorrectly employed, and the probability density function (pdf) required to extrapolate to
10
−
6
has been chosen arbitrarily, often as the lognormal pdf for mathematical convenience. Although the lognormal pdf may be an acceptable approximation for a database of concretes with very different strengths, it is shown to be physically impossible to model the strength distribution of one-and-the-same concrete (i.e., a concrete of the same design strength and composition). These traditional concepts have rendered the current failure probability predictions of the structural safety and reliability software for reinforced concrete structures meaningless. However, experience of many decades shows that the frequency of structural failures has not been excessive. The explanation is that many designs must have had excessive safety margins, thus becoming uneconomical, while the benefit of sophisticated commercial software applicable to the randomness of applied loads gets wasted. A sine qua non of the remedy is that the values of the coefficient of variation of the database and of the offset of the database mean from the code equation accompanying each design code equation must be revealed. This could be done in the code Commentary.
This article examines the theoretical prerequisites for establishing quantitative limits for the technical condition of reinforced concrete structures (limited serviceability and emergency), expressed as fractions of the design bearing capacity. It is noted that current regulatory documents, including GOST 31937, lack direct recommendations on the permissible reduction in bearing capacity due to defects.
The results of a summary of experimental data are presented, confirming the presence of a safety margin of up to 30% and a deformability margin of up to 50%, provided that regulatory design requirements are met. An analytical justification for the technical condition limits is provided based on a comparison of the calculated bending moment according to SP 63.13330 and the ultimate actual moment achieved with full realization of the curvilinear stress diagram in the compressed zone of concrete. A ratio in the range of 0.7–0.77 was obtained for a rectangular diagram and 0.55–0.77 for a triangular diagram. An analysis is provided of the reserves incorporated in the reliability factors for materials, operating conditions, and responsibility, as well as the performance characteristics of bending reinforced concrete elements in the ultimate limit state. Practical limit values were proposed: 0.9 for a limited serviceability condition (a 10% reduction in bearing capacity from the design value); and 0.75 for an emergency condition (a 25% reduction), which is consistent with the analysis of experimental and theoretical data.
V. S. Fedorov, I. A. Terekhov, D. P. Leletko· Building and reconstruction· 0 citations
Introduction: Cross-laminated timber structural elements are being actively introduced into the construction practice of residential and public buildings. A special factor in the design of CLT structures is the principles of ensuring their reliability, since a large amount of statistical data on the safety level of such structures has not yet been accumulated due to their relative novelty. Objective of the study is to develop an algorithm for probabilistic analysis of a bending CLT roof slab over a given service life based on the deflection criterion (linear displacements). Methods: The reliability indicator of a CLT roof slab is taken as the probability of failure-free operation, which is estimated by frequency based on random variable generation using the Monte Carlo method, employing an adopted mathematical model of the limit state. The numerical approach to reliability assessment, based on an analytical expression of the limit state, is the most effective approach due to the simplicity of algorithm implementation and reliable results when using various types of random variables. Results: An algorithm has been developed to evaluate the probability of failure-free operation of a CLT roof slab based on the deflection criterion when designing the panel for a design service life. Probabilistic analysis allows selecting the most efficient structural solution for a CLT roof slab for a given reliability index β. The influence of lamella thickness tolerance factors of the CLT roof slab on reliability (probability of failure-free operation) has been established.
S. Solovev, V. Puchkov, A. Soloveva· Architecture and Engineering· 0 citations
Fracture failure of girth welds in high-grade steel pipelines poses a critical threat to pipeline integrity. Leveraging enhanced digitalization in pipeline engineering, a statistical database has been developed to support reliability analysis based on actual operational data. This study utilizes real project data to analyze the failure probability and key influencing factors of girth welds containing crack defects, thereby providing theoretical support for safety design and risk management. To overcome the conservatism of traditional deterministic methods, a probabilistic reliability model was established, incorporating a modified PRCI-CRES ultimate tensile strain criterion. Addressing the inefficiency of standard Monte Carlo (MC) simulation in high-dimensional low-probability contexts, an efficient Hamiltonian Monte Carlo-Subset Simulation (HMC-SS) strategy was introduced. Results show that HMC-SS improves computational efficiency by 99.95% over MC, with only 0.90% relative error. Key findings include: crack depth has the strongest influence – variation from 0.92 mm to 3.68 mm, which increases failure probability by 103 times; the strength matching coefficient is dominant, and higher values reduce failure risk; strain demand exhibits a positive correlation with failure probability and couples with material properties. It is concluded that high- or equal-strength material matching should be emphasized in welding, and reliability-informed design should account for multi-parameter interactions to ensure global safety.
Kai Yang, Kaihong Wang, Bin Wang et al.· SAE technical paper series· 0 citations
Despite the advantages of combined vertical, moment, and horizontal (VMH) failure envelopes, serviceability was not adequately considered in previous studies, leading to the introduction of serviceability-based "design envelopes" in current research, as a complement to conventional failure envelopes. This study employs three-dimensional finite element analysis to develop design and failure envelopes for square raft and cubic embedded block foundations under VMH loading. The numerical investigation, validated against well-documented benchmarks, uses the Hardening Soil model with small-strain stiffness (HSS). The envelopes were developed using probe tests associated with the dominant system parameters: breadth (2.5 to 25 m), embedment depth to breadth ratio (1, 2, and 3), and c-ϕ subsoil relative density (loose, medium, and dense). The results demonstrate that serviceability limits often govern foundation design, since the design envelopes are significantly smaller than the associated failure envelopes. Embedment depth is identified as a significant parameter that influences the transition from base-bearing to three-dimensional resistance mechanisms and enhances moment and horizontal capacities. The study examines the relationship among foundation geometry, embedment ratio, and subsoil strength in shaping failure and design envelopes. Multivariate regression analysis was used to derive mathematical equations for ellipsoidal failure and design envelopes. Overall, the findings challenge the traditional safety-factor paradigm and highlight the need for displacement-based design methodologies in modern foundation systems.
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