Nonlinear soil-structure interaction for buried pressure pipes under differential ground motion

Pipelines extend thousands of kilometers across wide geographic areas as a network to provide essential services for modern life. It is inevitable that pipelines must pass through unfavorable ground conditions, which are susceptible to natural disasters. This thesis investigates the behaviour of buried pressure pipelines experiencing ground distortions induced by normal faulting. A recent large database of physical modelling observations on buried pipes of different stiffness relative to the surrounding soil subjected to normal faults provided a unique opportunity to calibrate numerical tools. Three-dimensional finite element models were developed to enable the complex soil-structure interaction phenomena to be further understood, especially on the subjects of gap formation beneath the pipe and the trench effect associated with the interaction between backfill and native soils. Benchmarked numerical tools were then used to perform parametric analysis regarding project geometry, backfill material, relative pipe-soil stiffness and pipe diameter. Seismic loading produces a soil displacement profile that can be expressed by isoil, the distance between the peak curvature and the point of contraflexure. A simplified design framework based on this length scale (i.e., the Kappa method) was developed, which features estimates of longitudinal bending moments of buried pipes using a characteristic length, ipipe, the distance from peak to zero curvature. Recent studies indicated that empirical soil springs that were calibrated against rigid pipes are not suitable for analyzing flexible pipes, since they lead to excessive conservatism (for design). A large-scale split-box normal fault simulator was therefore assembled to produce experimental data for flexible PVC pipe responses to a normal fault. Digital image correlation (DIC) was employed to analyze the soil displacement field, and both optical fibres and conventional strain gauges were used to measure pipe strains. A refinement to the Kappa method was introduced to enable the calculation of axial strains as a function of pipe elongation induced by flexure and an approximation of the longitudinal ground deformations. A closed-form Winkler solution of flexural response was also derived to account for the distributed normal fault pattern. Finally, these two analytical solutions were evaluated against the pipe responses observed in the large-scale laboratory tests.

Polymer Fluid Dynamics: Continuum and Molecular Appoaches

To solve problems in polymer fluid dynamics, one needs the equation of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (1) one can write a continuum expression for the stress tensor in terms of kinematic tensors, or (2) one can select a molecular model that represents the polymer molecule, and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. In this review, we restrict the discussion primarily to the simplest stress tensor expressions or “constitutive equations” containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. The virtue of studying the simplest models is that we can discover some general notions as to which types of empiricisms or which types of molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows. These are the flows that are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.