Local buckling of pipeline walls is a common failure mode for buried pipelines crossing reverse faults. The damage evolution of pipelines from initial buckling to severe failure under reverse fault displacement is closely related to soil properties, fault mechanism, and pipeline geometry. The performance-based design methodology proposed by the Pacific Earthquake Engineering Research Center has become well-recognized worldwide. However, current safety-based design codes for buried steel pipelines generally provide operable limits corresponding to the initiation of local buckling of the pipeline walls, and cannot be used to effectively assess the damage states and performance levels of pipelines. To address the local buckling of pipeline walls under fault displacement, a performance criterion is proposed based on the critical compressive strain and the change rate of pipeline compressive strain. Three performance levels corresponding to pipeline wall local buckling are identified, namely, buckling initiation, buckling development, and buckling failure. Moreover, the ductility coefficient that characterizes the nonlinear behavior of the pipeline wall prior to buckling failure is proposed in this study to quantify the damage state threshold values. Three-dimensional finite element models of the largediameter pipeline crossing a reverse fault are developed and validated against the existing experiment study. Parametric analysis is performed to comprehensively assess the effects of pipeline burial depth, fault mechanism, and pipeline geometry on the performance of the buried steel pipeline under reverse fault displacement. Finally, the empirical equation for critical displacements between performance levels under different conditions is developed. The numerical results indicate that as the diameter-to-thickness ratio and burial depth of the pipeline increase, the structure ductility of the pipeline wall prior to buckling failure decreases. The structural ductility of the pipeline wall increases by 94.7 % as the fault dip angle increases from 30 degrees to 90 degrees. Moreover, the structural ductility increases when the internal pressure increases from 0 MPa to 6 MPa, but decreases as the internal pressure changes further from 6 MPa to 12 MPa.

The absence of a defined allowable pile ductility in integral abutment bridges (IABs) creates a critical gap in determining the maximum safe bridge length. This paper introduces a design aid procedure to assist bridge engineers in establishing the length limits of jointless bridges. Numerical and analytical approaches were used in formulating the design aid procedure. A total of 66 finite difference models were established to obtain pile equivalent cantilever length considering various design parameters (soil stiffness, pile size, pile orientation, axial compressive load, and lateral displacement magnitude). The analytical approach incorporates a strain compatibility and equilibrium model to generate moment -curvature diagrams and load -deflection curves for standard HP sections commonly used in IABs construction. The validity of the developed design aid procedure was examined and tested with available experimental and numerical results. Lateral buckling displacement capacity of HP sections ranged from 50 to 100 mm (2 - 4 in.). Based on these displacement capacities, length limits for IABs were established and compared with existing studies. The maximum length limits for steel integral bridges fall within the range of 162 - 320 m (530 - 1050 ft), while concrete integral bridges have limits ranging from 210 to 390 m (680 - 1285 ft). These limits depend on factors such as pile size, soil stiffness, and climate conditions.