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.

Permanent deformation and uplift caused by fault rupture is one of the most significant hazards posed by earthquakes on the built environment. In this paper, we use smoothed particle hydrodynamics (SPH) to explore the effects of soil layering or stratification on the trajectories and deformation patterns caused by rupturing reverse faults in bedrock, as well as in the foundations of engineered earth structures. SPH is a continuum meshfree numerical method highly adept at modeling large deformation problems in geotechnics. Through the use of constitutive models involving softening behavior as well as critical state type models, we isolate the effects of rigid body rotation from critical state behavior of soil in helping explain the frequently observed rotation of shear bands emanating from the bedrock fault. This analysis is facilitated by the fact that the SPH method allows us to track the propagation of shear bands over substantial amounts of vertical uplift (more than 50% of the total height of the soil deposit), far beyond many previous computational studies employing the finite element method (FEM). We observe and characterize various emergent features including fault bifurcations, stunted faults, and tension cracking, while providing insights into practical guidelines regarding the potential surface distortion width, and the critical amount of fault displacement required for surface rupture depending on the multilayered constitution of the soil deposit. Finally, we predict the expected amount of surface distortion and internal damage to earthen embankments depending on varying fault location and soil makeup.

Damage to the overlying soil caused by fault misalignment poses a significant threat to the structural safety of buried pipelines crossing faults, which is a non-negligible factor in the design of underground pipelines in complex environments. Existing research rarely involves analytical solutions for the force and deformation of pipeline structures under normal and reverse fault movements, and theoretical studies on fault-pipeline interactions often treat the pipeline structure as continuous, with little consideration for the influence of pipeline joints. Firstly, soil displacement curves for both normal and reverse faults are derived using the erf and erfc functions, based on a simplified SSR (stationary zone, shearing zone, rigid body zone) soil deformation model. Secondly, the deformation and internal force of the buried pipeline structure are solved using the two-parameter Pasternak foundation model and the finite difference method. Finally, the theoretical analytical solution is compared with existing experimental and 3D numerical simulation results, showing good agreement. In addition, sensitivity analyses are conducted for key physical parameters, including fault dip, fault-pipeline inter location, and joint rotation stiffness. The results show that fault dip will change the position of the pipeline displacement curve and axial stress curve, but the maximum displacement and maximum axial stress are basically identical. The inter of the fault and the pipeline will not only change the shape of the pipeline displacement curve and axial stress curve, but also alter the maximum axial stress. With the increase of joint rotation stiffness, the maximum axial stress value of the pipeline increases. When the joint rotation stiffness is large enough, the jointed pipeline can be calculated as if it is continuous.

Tunnels subjected to reverse fault dislocation undergo severe structural damage, and their mechanical response and failure characteristics play a key role in seismic fortification efforts. This paper investigates the mechanical responses and failure characteristics exhibited by tunnels subjected to reverse faulting using theoretical analysis and numerical simulations. A theoretical model is established for analysing the bending moment, shear force, and safety factor of the tunnels under reverse fault dislocation. The nonuniform fault displacement, fault zone width, and nonlinear soil-tunnel interaction is applied in the proposed theoretical model, significantly improving the analysis accuracy and range of applicability. The corresponding numerical simulation based on the XFEM (extended finite element method) is carried out, and the proposed theoretical model is verified by the numerical results. The theoretical results demonstrate excellent agreement with the numerical results when nonuniform fault displacement is considered. A parametric analysis is presented in which the effects of the maximum fault displacement, fault zone width, and ratio of the maximum fault displacement of the footwall to the hanging wall are investigated. The results show that the ultimate fault displacement for compression-bending failure of the tunnel subjected to reverse fault dislocation is estimated to be approximately 30 cm, while the ultimate displacement for shear failure stands at 20 cm. Variations in the fault displacement ratio yield alterations in the distribution pattern and peak values of internal forces, together with shifts in the potential failure ranges of the footwall and hanging wall. Additionally, an initial crack emerged on the tunnel crown near the fault plane, followed by a second crack on the tunnel invert. Upon reaching a fault displacement of approximately 40 cm, the crack fully traverses the entire tunnel lining.