An analytical method for strength verification of buried steel pipelines at normal fault crossings

The complex problem of strength verification of a buried steel pipeline crossing the trace of a normal active fault is treated analytically, and a refined methodology for the calculation of the axial and bending pipeline strains is presented. In essence, the proposed methodology extends the analytical methodology originally proposed by Karamitros et al. [1] for the simpler case of strike-slip fault crossings. The modifications introduced to the original methodology are first identified, following a thorough examination of typical results from advanced 3D nonlinear numerical analyses, and consequently expressed via an easy to apply solution algorithm. A set of similar numerical analyses, performed for a wide variety of fault plane inclinations and intersection angles between the pipeline axis and the fault trace, is used to check the accuracy of the analytical predictions. Fairly good agreement is testified for pipeline strains up to 1.50–2.00%. It is further shown that, although the methodology proposed herein applies strictly to the case of right intersection angles, it may be readily extended to oblique intersections, when properly combined with existing analytical solutions for strike-slip fault crossings (e.g. [1]).     

A semi-analytical approach to a nonlinear stress–strain analysis of buried steel pipelines crossing active faults

In the present paper a semi-analytical methodology for a nonlinear stress–strain analysis of buried steel pipelines at active fault crossings is presented and verified. The developed model introduces a number of critical refinements to the existing methodologies which extend the application area of analytical models in pipeline design. In particular, a strike-slip and normal-slip fault crossings can be analyzed taking into account material and large displacement nonlinearities, nonlinear pipe–soil interaction. The proposed model is verified against the results by other authors and numerical results, obtained with the finite element method.     

Sensitivity analysis of site effects on response spectra of pipelines

In this paper, a numerical sensitivity analysis of the site effect on dynamic response of pipelines embedded in some idealised soil deposits resting on a halfspace covering a wide range of soil profiles encountered in practice and subjected to vertically propagating shear waves, is presented. The power spectrum of the lateral differential displacement between two distant points due to the site effect is formulated analytically by using an analytical amplification function of a viscoelastic inhomogenous soil profile overlying either a compliant halfspace or a bedrock, represented by a more realistic continuous model. Also, Kanai-Tajimi spectrum parameters are estimated and expressed analytically from the soil profile model. Finally, results in the form of stochastic response spectrum of pipelines, for different key soil and pipeline parameters, are given and discussed.     

Mechanical behavior of buried steel pipes crossing active strike-slip faults

The present paper addresses the mechanical behavior of buried steel pipes crossing active strike-slip tectonic faults. The pipeline is assumed to cross the vertical fault plane at angles ranging between zero and 45 degrees. The fault moves in the horizontal direction, causing significant plastic deformation in the pipeline. The investigation is based on numerical simulation of the nonlinear response of the soil–pipeline system through finite elements, accounting for large strains and displacements, inelastic material behavior of the pipeline and the surrounding soil, as well as contact and friction on the soil–pipe interface. Steel pipes with D/t ratio and material grade typical for oil and gas pipelines are considered. The analysis is conducted through an incremental application of fault displacement. Appropriate performance criteria of the steel pipeline are defined and monitored throughout the analysis. The effects of various soil and line pipe parameters on the mechanical response of the pipeline are examined. The numerical results determine the fault displacement at which the specified performance criteria are reached, and are presented in diagram form, with respect to the crossing angle. The effects of internal pressure on pipeline performance are also investigated. In an attempt to explain the structural behavior of the pipeline with respect to local buckling, a simplified analytical model is also developed that illustrates the counteracting effects of pipeline bending and axial stretching for different crossing angles. The results from the present study can be used for the development of performance-based design methodologies for buried steel pipelines.     

Methodology for the development of analytical fragility curves for retrofitted bridges

Fragility curves for retrofitted bridges indicate the influence of various retrofit measures on the probability of achieving specified levels of damage. This paper presents an analytical methodology for developing fragility curves for classes of retrofitted bridge systems. The approach captures the impact of retrofit on the vulnerability of multiple components, which to date has not been adequately addressed, and results in a comparison of the system fragility before and after the application of different retrofit measures. Details presented include analytical modeling, uncertainty treatment, impact of retrofit on demand models, capacity estimates, and component and system fragility curves. The findings indicate the importance of evaluating the impact of retrofit not only on the targeted response quantity and component vulnerability but also on the overall bridge fragility. As illustrated by the case study of a retrofitted multi‐span continuous (MSC) concrete girder bridge class, a given retrofit measure may have a positive impact on some components, yet no impact or a negative impact on other critical components. Consideration of the fragility based only on individual retrofitted components, without regard for the system, may lead to over‐estimation or under‐estimation of the impact on the bridge fragility. The proposed methodology provides an opportunity to effectively compare the fragility of the MSC concrete bridge retrofit with a range of different retrofit measures. The most effective retrofit in reducing probable damage for a given intensity is a function of the damage state of interest. Copyright © 2008 John Wiley & Sons, Ltd.     

Domestic Well Capture Zone and Influence of the Gravel Pack Length

Domestic wells in North America and elsewhere are typically constructed at relatively shallow depths and with the sand or gravel pack extending far above the intake screen of the well (shallow well seal). The source areas of these domestic wells and the effect of an extended gravel pack on the source area are typically unknown, and few resources exist for estimating these. In this article, we use detailed, high-resolution ground water modeling to estimate the capture zone (source area) of a typical domestic well located in an alluvial aquifer. Results for a wide range of aquifer and gravel pack hydraulic conductivities are compared to a simple analytical model. Correction factors for the analytical model are computed based on statistical regression of the numerical results against the analytical model. This tool can be applied to estimate the source area of a domestic well for a wide range of conditions. We show that an extended gravel pack above the well screen may contribute significantly to the overall inflow to a domestic well, especially in less permeable aquifers, where that contribution may range from 20% to 50% and that an extended gravel pack may lead to a significantly elongated capture zone, in some instances, nearly doubling the length of the capture zone. Extending the gravel pack much above the intake screen therefore significantly increases the vulnerability of the water source.     

Earthquake fault‐induced surface rupture—A hybrid strong ground motion simulation technique and discussion for structural design

Unique to the near‐source region of a large earthquake is the occurrence of strong impulsive ground motion and surface faulting referred to as ‘fling‐step’ motion. The objective of this study is to synthesize broad‐band time histories over a wide range of frequencies by characterizing rupture directivity and fling effects from the comprehensive strong motion database of the near‐fault Chi‐Chi event. To aid in the generation of these special types of ground motions, a hybrid modeling technique is introduced based on the stochastic finite‐fault radiation method and an efficient analytical approach to incorporate the observed low‐frequency features in the records close to the ruptured fault. The results show that the overall agreement among the developed hybrid methodology and recorded waveforms and response spectra is quite satisfying. A brief discussion on the design of infrastructures near seismic fault is also included. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical evaluation of the dynamic response of pipelines to vibrations induced by the operation of a pavement breaker

This paper studies the response of pipelines to vibrations induced by the operation of a pavement breaker during the rehabilitation of concrete pavements. An efficient two-and-a-half-dimensional (2.5D) formulation is employed, where the geometry of the structure and the soil is assumed to be invariant in the longitudinal direction, allowing for a Fourier transform of the longitudinal coordinate y along the structure to the wavenumber k_y. The dynamic soil–structure interaction problem is solved by means of a 2.5D coupled finite element–boundary element (FE–BE) method using a subdomain formulation. The numerical model is verified by means of results available in the literature for a buried pipeline subjected to incident P- and SV-waves with an arbitrary angle of incidence. The presented methodology is capable to incorporate any type of incident wave field induced by earthquakes, construction activities, traffic, explosions or industrial activities. The risk of damage to a high pressure steel natural gas pipeline and a concrete sewer pipe due to the operation of a pavement breaker is assessed by means of the 2.5D coupled FE–BE methodology. It is observed that the stresses in the steel pipeline due to the operation of the pavement breaker are much lower than those induced by the operating internal pressure. The steel pipeline behaves in the linear elastic range under the combined effect of the loadings, indicating that damage to steel pipelines close to the road due to the operation of a pavement breaker is unlikely. The maximum principal stress in the concrete pipe, on the other hand, remains only slightly lower than the specified tensile strength. The decision to use a pavement breaker should hence be taken with care, as its operation may induce tensile stresses in concrete sewer pipes which are of the same order of magnitude as the tensile strength of the concrete. Assessing the risk of damage by means of vibration guidelines based on the peak particle velocity (PPV) gives, for the particular cases considered, qualitatively similar results.     

Centrifuge modeling of buried continuous pipelines subjected to normal faulting

Seismic ground faulting is the greatest hazard for continuous buried pipelines.Over the years,researchers have attempted to understand pipeline behavior mostly via numerical modeling such as the finite element method.The lack of well-documented field case histories of pipeline failure from seismic ground faulting and the cost and complicated facilities needed for full-scale experimental simulation mean that a centrifuge-based method to determine the behavior of pipelines subjected to faulting is best to verify numerical approaches.This paper presents results from three centrifuge tests designed to investigate continuous buried steel pipeline behavior subjected to normal faulting.The experimental setup and procedure are described and the recorded axial and bending strains induced in a pipeline are presented and compared to those obtained via analytical methods.The influence of factors such as faulting offset,burial depth and pipe diameter on the axial and bending strains of pipes and on ground soil failure and pipeline deformation patterns are also investigated.Finally,the tensile rupture of a pipeline due to normal faulting is investigated.     

Stormwater capture and antecedent moisture characteristics of permeable pavements

An approach based on individual rainfall events is introduced to mathematically describe the hydrologic responses and estimate the stormwater capture efficiencies of permeable pavement systems (PPSs). A stochastic model describing the instantaneous dynamic water balance of a PPS is established, from which the probability distribution of the antecedent moisture content of the PPS at the beginning of a rainfall event is analytically derived. Based on this probability distribution and the event‐based approach, an analytical equation that can be used for estimating the stormwater capture efficiencies of PPSs is also derived. The derived analytical equation is verified by comparing its results with those from continuous simulations for a wide range of PPSs with different sizes and underlying soils and operating under various climate conditions. It was found that the antecedent moisture contents of PPSs at the test locations are usually fairly close to zero, suggesting that PPSs at these locations are always almost empty at the start of a rainfall event. The derived analytical equation accounts for many key processes influencing the behaviour and operation of PPSs; it may serve as an easy‐to‐use tool that is essential for the planning and design of PPSs.     

A refined seismic analysis and design of buried pipeline for fault movement

Some lifelines, such as gas and oil transmission lines and water and sewer pipelines, have been damaged in recent earthquakes. The damages of these lifelines may cause major, catastrophic disruption of essential services for human needs. Large abrupt differential ground movements that result from an active fault present one of the most severe effects of an earthquake on a buried pipeline system. Although simplified analysis procedures for buried pipelines across strike-slip fault zones that cause tensile failure of the pipeline have been proposed, the results are not accurate enough because of several assumptions involved, such as the omission of flexural rigidity of the pipe, simplification of soil resistant characteristics, etc. Note that the omission of flexural rigidity cannot satisfy equilibrium conditions for pipelines across a ‘reverse’ strike-slip fault that causes compressions in the pipeline. This paper presents a refined analysis procedure for buried pipelines that is applicable to both strike-slip and reverse strikeslip faults after modifying some of the assumptions used previously. Based on the analytical results, this paper also discusses the design criteria for buried pipelines which are subjected to various fault movements. Parametric responses of buried pipeline for various fault movements, angles of crossing, buried depths and pipe diameters are presented.     

Finite element analysis of buried steel pipelines under strike-slip fault displacements

The present paper investigates the mechanical behavior of buried steel pipelines, crossing an active strike-slip tectonic fault. The fault is normal to the pipeline direction and moves in the horizontal direction, causing stress and deformation in the pipeline. The interacting soil–pipeline system is modelled rigorously through finite elements, which account for large strains and displacements, nonlinear material behavior and special conditions of contact and friction on the soil–pipe interface. Considering steel pipelines of various diameter-to-thickness ratios, and typical steel material for pipeline applications (API 5L grades X65 and X80), the paper focuses on the effects of various soil and pipeline parameters on the structural response of the pipe, with particular emphasis on identifying pipeline failure (pipe wall wrinkling/local buckling or rupture). The effects of shear soil strength, soil stiffness, horizontal fault displacement, width of the fault slip zone are investigated. Furthermore, the influence of internal pressure on the structural response is examined. The results from the present investigation are aimed at determining the fault displacement at which the pipeline fails and can be used for pipeline design purposes. The results are presented in diagram form, which depicts the critical fault displacement, and the corresponding critical strain versus the pipe diameter-to-thickness ratio. A simplified analytical model is also developed to illustrate the counteracting effects of bending and axial stretching. The numerical results for the critical strain are also compared with the recent provisions of EN 1998-4 and ASCE MOP 119.     

Analytical solution of the solute transport equation for the binary homovalent ion exchange in groundwater

A binary homovalent ion exchange transport model governed by local chemical equilibrium is considered for a one-dimensional, steady flow in a homogeneous soil column. An analytical solution of the aqueous concentration distribution for the convex exchange is obtained by applying nonlinear shock wave theory. The main nonlinear feature is the breaking of fronts into shock waves. The corresponding mathematical theory is the method of characteristics with a special treatment of shock waves. The wave velocity and front thickness are also obtained to illustrate the front propagation and structure. The derivation of the solution presented may offer a wide range of application opportunities and may also provide a good approach for solving the binary heterovalent exchange transport model.     

Methodology for estimating human perception to tremors in high-rise buildings

Human perception to tremors during earthquakes in high-rise buildings is usually associated with psychological discomfort such as fear and anxiety. This paper presents a methodology for estimating the level of perception to tremors for occupants living in high-rise buildings subjected to ground motion excitations. Unlike other approaches based on empirical or historical data, the proposed methodology performs a regression analysis using the analytical results of two generic models of 15 and 30 stories. The recorded ground motions in Singapore are collected and modified for structural response analyses. Simple predictive models are then developed to estimate the perception level to tremors based on a proposed ground motion intensity parameter—the average response spectrum intensity in the period range between 0.1 and 2.0 s. These models can be used to predict the percentage of occupants in high-rise buildings who may perceive the tremors at a given ground motion intensity. Furthermore, the models are validated with two recent tremor events reportedly felt in Singapore. It is found that the estimated results match reasonably well with the reports in the local newspapers and from the authorities. The proposed methodology is applicable to urban regions where people living in high-rise buildings might feel tremors during earthquakes.     

Reduction of steady-state forced vibrations of structures with dynamic absorbers

In the paper the problem of reduction of the steady-state response of a lightly damped structure to periodic excitation is considered. The primary structure, which has arbitrary distributions of mass, stiffness and damping, is subjected to periodic load with the fundamental frequency varying in a wide range that may include several resonant peaks of the amplitude-frequency response. A number of passive absorbers are applied simultaneously to the main structure. A general formulation of the dynamic absorber design methodology is presented, based on independent design of conventional absorbers, taking into account the selected modal systems of the original structure and the selected harmonic components of the excitation. In order to cover the losses in the vibration reduction, resulting from the couplings in the primary structure–the set of absorbers system and from the remaining harmonic components of the excitation, the mass of modal dynamic absorbers is increased properly. The methodology developed was verified on several numerical examples; one of them is presented in the study.     

A practical method for analysis of river waves and for kinematic wave routing in natural channel networks

The behaviour of river waves is described using a simplified dimensionless form of the momentum equation in conjunction with the continuity equation. Three dimensionless parameters were derived based on a quantitative linear analysis. These parameters, which depend on the Froude number of the steady uniform flow and the geometric characteristics of the river, permit quantification of the influence of inertia and pressure in the momentum equation. It was found that dynamic and diffusion waves occur mainly on gentle channel slopes and the transition between them is characterized by the Froude number. On the other hand, the kinematic wave has a wide range of applications. If the channel slope is greater than 1%, the kinematic wave is particularly suitable for describing the hydraulics of flow. Since slopes in natural channel networks are often greater than 1%, an analytical solution of the linearized kinematic wave equation with lateral inflow uniformly distributed along the channel is desirable and was therefore derived. The analytical solution was then implemented in a channel routing module of an existing simple rainfall–runoff model. The results obtained using the analytical solution compared well with those obtained from a non‐linear kinematic wave model. Copyright © 2000 John Wiley & Sons, Ltd.     

对一储配站输气管道的抗震鉴定与震害预测

基于输气管道在以往地震中的地震灾害与抗震性能,对一储配站的输气管道进行了抗震鉴定和震害预测。首先说明地下管道的3种抗震鉴定方法以及震害预测方法:规范法、近似法和反应位移法。然后具体说明了3种方法在输气管道抗震性能鉴定的应用,以可靠性理论为基础,采用抗震鉴定的综合分析方法进一步得到输气管道的震害预测结果。     

Pipe–soil interaction and pipeline performance under strike–slip fault movements

The performance of pipelines subjected to permanent strike–slip fault movement is investigated by combining detailed numerical simulations and closed-form solutions. First a closed-form solution for the force–displacement relationship of a buried pipeline subjected to tension is presented for pipelines of finite and infinite lengths. Subsequently the solution is used in the form of nonlinear springs at the two ends of the pipeline in a refined finite element model, allowing an efficient nonlinear analysis of the pipe–soil system at large strike–slip fault movements. The analysis accounts for large strains, inelastic material behavior of the pipeline and the surrounding soil, as well as contact and friction conditions on the soil–pipe interface. The numerical models consider infinite and finite length of the pipeline corresponding to various angles β between the pipeline axis and the normal to the fault plane. Using the proposed closed-form nonlinear force–displacement relationship for buried pipelines of finite and infinite length, axial strains are in excellent agreement with results obtained from detailed finite element models that employ beam elements and distributed springs along the pipeline length. Appropriate performance criteria of the steel pipeline are adopted and monitored throughout the analysis. It is shown that the end conditions of the pipeline have a significant influence on pipeline performance. For a strike–slip fault normal to the pipeline axis, local buckling occurs at relatively small fault displacements. As the angle between the fault normal and the pipeline axis increases, local buckling can be avoided due to longitudinal stretching, but the pipeline may fail due to excessive axial tensile strains or cross sectional flattening. Finally a simplified analytical model introduced elsewhere, is enhanced to account for end effects and illustrates the formation of local buckling for relative small values of crossing angle.     

Numerical validation of analytical solutions and their use for equivalent-linear seismic analysis of circular tunnels

The first part of this paper presents an extensive validation of four analytical solutions for the seismic design of circular tunnels. The validation is performed with a quasi-static finite element (FE) model which conforms to the assumptions of the analytical solutions. Analyses are performed for a wide range of flexibility ratios, slippage conditions at soil–lining interface, assuming both drained and undrained behaviour. Based on the numerical predictions the relative merits of the considered analytical solutions are discussed and recommendations are given for their use in design. The second part of this paper explores the use of equivalent linear soil properties in analytical solutions as an approximate way of simulating nonlinearity. The results of equivalent linear site response analyses are used as an input for the analytical solutions. The comparison of the analytical predictions with nonlinear numerical analysis results is very satisfactory. The results of this study suggest that analytical solutions can be used for preliminary design using equivalent linear properties and the corresponding compatible strain as an approximate way of accounting for nonlinear soil response.     

A marching in space and time (MAST) solver of the shallow water equations. Part II: The 2D model

A novel methodology for the solution of the 2D shallow water equations is proposed. The algorithm is based on a fractional step decomposition of the original system in (1) a convective prediction, (2) a convective correction, and (3) a diffusive correction step. The convective components are solved using a Marching in Space and Time (MAST) procedure, that solves a sequence of small ODEs systems, one for each computational cell, ordered according to the cell value of a scalar approximated potential. The scalar potential is sought after computing first the minimum of a functional via the solution of a large linear system and then refining locally the optimum search. Model results are compared with the experimental data of two laboratory tests and with the results of other simulations carried out for the same tests by different authors. A comparison with the analytical solution of the oblique jump test has been also considered. Numerical results of the proposed scheme are in good agreement with measured data, as well as with analytical and higher order approximation methods results. The growth of the CPU time versus the cell number is investigated successively refining the elements of an initially coarse mesh. The CPU specific time, per element and per time step, is found out to be almost constant and no evidence of Courant–Friedrichs–Levi (CFL) number limitation has been detected in all the numerical experiments.