Nonlinear Analysis of the Surface Faulting Effects on the Buried Pipelines: the Application of the Combination of Finite Difference and Multivariable Methods

In current modern cities, the use of buried pipelines in the conveying of vital fluids such as water, oil, and gas have become very important. Investigations on the behavior of the buried pipelines after the occurrence of the severe earthquakes have indicated that one of the primary sources of the failures of these kinds of linear structures were due to surface fault rupture. Therefore, if the buried pipelines are designed and implemented correctly, the permanent ground displacement due to the movement of the bedrock fault will not lead to such rupture of the pipes. On this basis, different researchers have concentrated their studies on investigating the interaction of pipe and soil during the permanent ground displacement. Due to the difficulty and cost of laboratory tests on this phenomenon, the number of available experimental data is very few. On the other hand, analytical studies have various limitations and complexities that have made it difficult for engineers to use these methods. In addition, numerical methods used to study the interaction of pipes and faults are mostly prepared for academic environments. These numerical approaches usually need the knowledge of soil or pipe advanced constitutive models and require the familiarity with mathematical parameters necessary for the convergence of the computational efforts.
In order to investigate the behavior of buried pipes against faulting displacement, in this paper, a numerical method has been developed by combining finite difference and Newton multivariable techniques. The equilibrium equation of forces in x and y directions along with the equilibrium equation of bending moment for an infinite section of the pipe under the influence of the displaced soil pressure has been obtained first. Then the system of equations for all of the discretized nodes of a pipeline has been solved using the proposed hybrid method. The proposed method simultaneously considers the nonlinear behavior of pipes, soil equivalent springs, and large strains in the beam-spring model. In addition, to more precisely assess the shear factor in the beam behavior, the Timoshenko beam model has been applied to model the pipe.
The validity of the proposed method has been performed using the results of a laboratory centrifuge test on HDPE pipe and 90° normal fault. In addition, this hybrid method is also validated with the results of a finite element numerical analysis on 70° normal fault and API5L-X65 oil transfer pipe. Comparison of the obtained results for different parameters such as longitudinal strains, settlement, and flexural bending of the pipes shows that the presented numerical method is very suitable in predicting the interaction behavior of pipes against dip-slip faults. At the same time, a lower computational effort has been required to arrive in the final answers. In addition, using the proposed numerical method, the effect of fault zone width with values equal to 0.001, 10, 30, 60, and 100 m on the behavior of a pipeline against a normal 70-degree fault has been investigated. The results of this study show that increasing the width of the fault zone significantly reduces the amount of tensile strain in the pipes. Also, increasing the width of the fault zone causes the pipe to rupture from two different points, while in the small fault width equal to 0.001 m, the pipe failure occurs only at one point. Maximum bending moment and pipe curvature also increased with decreasing fault width.