Reliability Calculation and Analysis of Influencing Factors for Girth Welds in High-Grade Steel Pipelines Based on HMC-SS

Weibull‐Based Probabilistic Analysis of Cracking Risk in Blast Furnace Hearth Carbon Bricks Under Thermomechanical Loading

Unexpected cracking of carbon bricks in blast furnace hearths remains a critical challenge for campaign safety and long service life, while deterministic criteria based solely on stress magnitude are insufficient to describe the stochastic fracture behavior of porous brittle materials. In this study, a three‐dimensional thermomechanical finite element model with explicit brick‐joint geometry is established, and a Weibull‐based probabilistic criterion is introduced to relate stress state to crack initiation risk. Joint width, hot‐face temperature, and the thermal conductivity of the ramming mix are systematically analyzed. The results show that joint width governs a transition in stress mode and thereby changes the calculated cracking‐risk index: at 0.1 mm, strong constraint causes radial tensile‐stress concentration near the hot face, with a local cracking‐risk index of 19.1%, whereas at 0.5 mm, weakened constraint promotes the simultaneous increase of radial and circumferential tensile stresses, raising the index to 24.4%; by comparison, a joint width of about 0.3 mm gives the lowest cracking‐risk index of 17.8%. Hot‐face temperature is identified as the dominant variable. The local cracking‐risk index reaches 36.81% at 1450 °C and increases sharply thereafter. The proposed framework provides guidance for joint design and thermal management of blast furnace hearth carbon bricks.

Reliability and Structural Performance Assessment of Solid Concrete Block Masonry Prisms using Compressive Strength Modelling and Monte Carlo Simulations

Solid concrete block masonry is widely used in construction, but its performance is affected by variability in material properties, workmanship, and block quality. Traditional deterministic design methods often fail to capture these uncertainties, potentially leading to unsafe designs. This research proposes a reliability approach to assess masonry prism compressive strength through the integration of predictive modelling and probabilistic analysis. The objective is to perform a reliability analysis of masonry prisms and determine the Probability of failure. Five cement-sand mortar ratios (1:3 to 1:7) were experimentally evaluated, and Multiple Linear Regression (MLR) models were developed to estimate prism strength as a function of block and mortar strengths. The developed regression equations were incorporated into a Monte Carlo simulation framework with 40,000 iterations to evaluate the Probability of failure and reliability index for a typical residential building configuration. Results indicate that the 1:3 mortar mix provides superior structural performance, yielding a probability of failure (𝑃𝑓) of 0.0479 and a reliability index (𝛽) of 1.66, satisfying the adopted target reliability criterion. Floor optimization analysis further revealed that the structure can safely support up to 14 floors while maintaining the adopted Probability of failure limit of 5%. The findings highlight the significant influence of material variability on masonry reliability and demonstrate the effectiveness of probabilistic methods for realistic safety assessment and performance-based masonry design.

Probabilistic safety assessment of the shear-friction and strut-and-tie methods for designing reinforced-concrete corbels according to ACI 318–19

Probabilistic modeling for reliability assessment of biaxial fatigue-induced crack growth in rail-mounted gantry main girder

Accurately assessing the probabilistic reliability of rail-mounted gantry main girder under biaxial fatigue-induced crack growth remains a critical challenge in port machinery. Traditional methods often struggle to characterize the coupled effects of multiaxial loading, accumulative plasticity, and stochastic crack propagation, leading to significant statistical deviations. In order to overcome these shortcomings, the present work introduces a new probabilistic framework that combines non‑dimensional interference theory with stochastic fracture mechanics. The methodology leverages applied mathematical techniques to model crack growth as a random process, incorporating uncertainties in initial defect distributions, material properties, and biaxial loading spectra. First, finite element simulations extract stress responses under biaxial alternating loads, while rainfall counting and Goodman’s correction derive equivalent load spectra. Second, a continuous probability distribution model for fatigue life is established by combining the material P-S-N curve with sample aggregation theory, enabling precise quantification of crack growth rates under variable amplitude stresses. Finally, the reliability of Q235 steel and 7075 aluminum alloy rail-mounted gantry main girder is evaluated through probabilistic failure assessments based on the Failure Assessment Diagram (FAD)and Weibull stress criteria. Results demonstrate that the proposed approach not only mitigates statistical biases from traditional load-equivalent analyses but also achieves a unified probabilistic characterization of fatigue life under biaxial coupling conditions. This research highlights the utility of mathematical modeling in advancing structural reliability analysis, providing a robust tool for risk-informed design and maintenance of port machinery structures.

Structural Reliability Assessment of Post-Weld Treatment Methods for Fatigue Life Extension of Aging Steel Bridges

The management of aging steel bridges poses significant challenges to bridge owners, who must maintain structural integrity under fatigue-induced deterioration while operating within limited maintenance budgets. Although post-weld treatment methods have demonstrated potential to improve fatigue performance, a probabilistic quantification of their comparative reliability benefits remain limited in literature. This study presents a probabilistic S-N based reliability approach to evaluate and compare as-welded condition and three post-weld treatment methods, including burr grinding/TIG, needle/hammer peening, and HFMI. The approach is applied to a welded steel detail under variable amplitude loading, incorporating uncertainties in the fatigue resistance, damage accumulation and stress modelling. The results show that post-weld treatments significantly extend service life. Furthermore, an analysis shows the potential of SHM also contributing to service life extension, however, subjected to a specific outcome probabilities

Key fracture criteria for damage tolerance assessment of high-strength metallic materials in marine environments

Abstract Marine corrosion and hydrogen-induced degradation significantly reduce the fracture toughness of high-strength metallic materials. Traditional safety assessments using air-measured toughness (KIC) often overlook coupled environmental effects, potentially overestimating performance and creating latent risks. This paper systematically reviews the definitions, engineering significance, and testing methodologies of key toughness parameters in fracture mechanics, including K IC, J IC, K ISCC, and K IEAC, and provides an in-depth analysis of their applicability in the damage tolerance assessment of high-strength materials within marine environments. Research on the fracture toughness of R6 grade anchor chain steel demonstrates that fracture toughness tests conducted under static immersion in corrosive media (3.5 % NaCl solution) do not align with actual service conditions. In contrast, fracture toughness values measured under low-rate loading in a hydrogen-saturated state (via pre-charging) are significantly lower than those obtained in air or simple corrosive environments. This experimental condition more effectively simulates the processes of hydrogen ingress, diffusion, and accumulation during long-term service. Therefore, this study proposes that new fracture toughness parameters, which fully reflect the synergistic influence of hydrogen-induced degradation and environmental corrosion, must be introduced into the damage tolerance assessment of high-strength metallic materials for marine engineering to ensure the reliability of structural fracture-prevention safety designs.