УНИВЕРСИТЕТ ПО АРХИТЕКТУРА, СТРОИТЕЛСТВО И ГЕОДЕЗИЯМеждународна научно-приложна конференция УАСГ2009

29-31 ОКТОМВРИ 200929-31 OCTOBER 2009

International Conference UACEG2009: Science & PracticeUNIVERSITY OF ARCHITECTURE, CIVIL ENGINEERING AND GEODESY

EARTHQUAKE-INDUCED BEHAVIOUR OF BURIED PRESSURE PIPELINES: STATE-OF-THE-ART

I. MODELLING OF PHYSICAL PHENOMENA AND METHODS OF ANALYSIS

S. Petkova1, D. Kisliakov2

Keywords: Buried Pipelines, Seismic Excitation, Soil – Pipe Interaction, Fluid – Structure Interaction

Field of research: Lifeline Earthquake Engineering, Buried Pipelines

ABSTRACT

This work presents the first part of a systematic review of the main groups of computational models for buried pipelines under seismic excitation. On one hand, the aim of this analysis is to present the mostly used approaches in mechanical modelling of the earthquake-induced vibrations of buried pipelines. On the other hand, an attempt is made for identification of the existing gaps namely in modelling of the complex physical interaction phenomena related to the dynamic response of such pipelines. The focus of this first part of the performed review is on the features of the groups of theoretical models as well as on their key parameters describing the physics of the phenomena taking place. In this connection, some conclusions are drawn regarding well established approaches, difficulties and open tasks in the modelling process of this complicated field of coupled dynamic problems.

1. Introduction

Buried pipelines are part of the so-called lifelines which play a vital role as infrastructure components conveying and/or distributing energy, fluids, oil products and gas in present-day’s world. The pipelines in particular allow conveying water, fossil liquid fuels and liquid gas over long distances. Pressure pipelines are also often important part of large industrial facilities and hydropower systems.

1 Silvia Petkova; MSc CEng; Doctoral student at the Department of Hydraulic Engineering, UACEG, 1, Hristo Smirnenski Blvd., 1046 Sofia, BULGARIA, e-mail: silvia _ petkova @ mail . bg

2 Dimitar Kisliakov, Assoc. Prof. Dr., Department of Hydraulic Engineering, UACEG, 1, Hristo Smirnenski Blvd., 1046 Sofia, BULGARIA, e-mail: kiss _ fhe @ uacg . bg

There are different types of pressure pipelines depending on their function, construction material, pressure of the conveyed fluid, position relatively to the ground surface (underground, buried, above ground), etc.

In the following, buried pressure pipelines (penstocks) are considered as components of hydropower systems. They convey water and are constructed in a trench with backfill after the placement. Such pipelines are subjected to various dynamic impacts and loads during their operation like earthquakes, hydraulic transients, traffic, etc. However, only seismic excitation is further considered in this work.

In general, there are two main approaches for modeling the dynamic response of a buried pipeline during seismic excitation – stochastic and deterministic ones.

In the stochastic approach, the input excitation is a random event or process, respectively the pipeline’s response is also a random process. The advantages of this approach consist in the more realistic representation of the earthquake excitation as a random process, this model better corresponds to the nature of such event. This approach also allows more convenient accounting for other factors like material defects, imperfections, human mistakes and construction inaccuracies. The ground motion is modelled as a random process with a given power spectral density (PSD), and the spatial variation of the impact along the pipe structure is described by a correlation function, usually an exponentially decaying one [14]. A disadvantage constitutes the fact that some nonlinear interaction effects of the soil – pipe – fluid system cannot be accounted for.

In the deterministic approach, the time history of any ground motion parameter can be directly applied as input excitation of the structural model of the pipeline.

In general, the deterministic approach allows performing nonlinear analysis of some special effects during the seismic excitation, like imperfect soil – pipe contact and fluid – structure interaction. It is also more suitable for practical applications due to the usual formulation of the seismic excitation in design codes and guidelines in the form of design response spectrum.

The dynamic response of buried pipelines is different from that of buildings and other vertical structures. The differential motion between different parts of the pipeline over its length has to be considered since the length of the system is comparable to or larger than the seismic wave length. Furthermore, slippage may occur at the interface of the pipe – soil system, depending on the nonlinear restoring characteristics of the backfill, and the dynamic impact is kinematic rather than inertial one. There are also energy losses / damping effects due to: wave dissipation, friction and deterioration of soils. So, under seismic excitation, the response of a buried pipeline is controlled by the ground displacements / strains, predominantly in the axial direction, with dynamic effects being negligible according to the available knowledge [4].

2. Structural model of the pipeline

2.1 Continuous pipeline The mechanical model of a continuous pipeline has joints possessing higher strength

and stiffness relative to the pipe barrel. For example, a steel pipeline with welded (butt, single-lap or double-lap welded) joints is modelled as continuous pipeline. The construction (welded) joint of the continuous pipeline is often referred to as restrained joint.

The joint stiffness and rotation absorption capacity can be assumed the same as that of the pipe material and hence, the pipe can be regarded as a continuous beam, Fig. 1.

Fig.1. Three dimensional soil-pipe interactions and the mechanical model (ASCE, 1984)

2.2 Segmented pipelineA segmented pipeline has joints possessing lower strength and stiffness relative to the

pipe barrel. For example, cast iron pipes with caulked or rubber gasket joints, ductile iron pipe with rubber gasket joints, concrete or glass-reinforced pipes (GRP) with mechanical joints, etc. are usually modelled as segmented ones. The joints of the segmented pipes are generally referred to as unrestrained joints, Fig. 2.

Fig.2. Mechanical model of segmented pipeline with soil springs

3. Modeling of the earthquake excitation

The seismic excitation is modeled by means of seismic wave propagation, by ground displacement time history or ground acceleration time history (accelerogram).

The most common models governing the dynamic response of a buried pipeline to a propagating wave are shortly presented in the following.

Newmark developed a simplified procedure for estimating the ground strain. He considers a simple propagation wave with a constant wave shape whose acceleration, velocity and displacement time histories of two points along the propagation path are assumed to differ only by a time lag. This assumption is common to almost all deterministic procedures. The other assumptions are that the pipe inertia terms are small and may be neglected, and that there is no relative movement at the pipe – soil interface, hence the pipe strain equals the ground strain (perfect contact between the pipe and the soil). For such case, the maximum ground strain in direction of wave propagation is εg=Vm/C, where Vm is the maximum horizontal ground velocity and C is the propagation velocity of the seismic wave.

The maximum ground curvature, that is the second derivative of the transverse displacement with respect to the distance is Φg=Am/C2, where Am is the maximum ground acceleration perpendicular to the direction of wave propagation.

The soil deformations obtained by the Newmark’s method are relatively larger, leading to larger stresses and displacements in the pipe, respectively, thus leading to a more conservative design.

In [23], M.J.O’Rourke and X. Liu have systematized and presented procedures for evaluation of the response of buried pipeline subject to earthquake based on the Newmark’s approach.

In [12], Borsutzky and Lehmann have analysed the behavior of three-dimensional soil – pipe system subject to seismic waves. They used a two-steps domain reduction method, Fig. 3.

Fig.3. Domain Reduction Method

In the papers [29, 30, 31, 32] by S. Datta, A. Shah, K. Wong the dynamic response of buried pipeline has been investigated subjected to plane seismic P, SV – and Rayleigh waves traveling at an arbitrary angle to its axis. The reflection of the seismic waves at the free ground surface and the boundary surfaces is accounted for. Full dynamic interaction between the pipe and the surrounding soil is taken into account as well.

The pipe has been modeled as an empty, infinitely long, continuous, circular, cylindrical shell of small thickness. All contacts are assumed to be perfect, so that the displacements and tractions are continuous across the interface between regions. The governing equations of motion are presented and the solutions are obtained in terms of cylindrical eigenfunctions modified to satisfy the boundary conditions at the free surface ground.

Two problems have been analysed: (1) The pipe is surrounded by a homogeneous soft soil and (2) The pipe lays in a cylinder of soft soil, which is surrounded by a rocky material. The obtained results show generally that larger stresses and displacements occur in Case (1) than in Case (2). Thus, it may appear that if the problem is simplified by assuming a pipe surrounded entirely by a homogenous ground and then the larger estimates is considered, this will lead to a more conservative (i.e. safe) design implementation. The response is also found to be considerably influenced by the frequency of the incident wave and the depth of the embedment.

In [33, 34] by J. Luco and F. De Barros, a method is presented to obtain the three-dimensional harmonic response of a infinitely long cylindrical shell with circular cross section embedded in a layered visco-elastic half-space. The shell is subjected to P-, SV- and SH- waves affecting it at an oblique angle with respect to the axis.

The procedure combines an indirect integral representation for the field in the exterior half-space with a model of the pipeline based on Donnell shell theory. The integral representation of the soil is based on the use of moving Green’s functions for the layered half-space. Extensive literature survey has been also performed, and comparisons with previous results of two- and three-dimensional models are presented.

In other works [46], the incident impacts are modeled by ground displacement or acceleration time histories.

4. Soil – structure interaction

For buried pipelines, seismic hazards can be classified as either wave propagation hazards or permanent ground deformation (PGD) ones. During the seismic wave propagation, induced soil strains are transmitted to the pipeline which may rupture in tension or buckle in compression. Permanent ground movements include surface faulting, lateral spreading due to liquefaction, and landsliding [3, 4, 13, 23, 25, 26, 27, 28 ].

For understanding the behaviour of a buried pipeline under seismic excitation, an accurate (i.e. realistic) computational model of the soil – pipe system needs to be found in order to take into account the dynamic response of the pipe, the material features and the nature of the earthquake impact.

In [14], Akiyoshi studied the effect of frictional interaction between a pipe and the surrounding soil. Slippage of buried pipe has been verified in a simple test, using an experimental setup and an analytical procedure.

Static and dynamic experiments have been carried out. The results from static experiments executed with very slow axial movement of the pipe show almost Coulomb friction at the soil-pipe interface, Fig. 4. The skin friction around the pipe in dynamic tests shows a combination of frictional force of the Coulomb type and an elastic restoring force. The assumptions made here are that the slippage of frictional type is given independently of the elastic interaction between the soil and the pipe, i.e. all input energy is consumed in the response of the pipes without generating reflected waves from the pipe surface, and along the pipe axis only sinusoidal P-wave propagates.

Fig.4. Representation of a buried frictional pipe and the relationship between frictional force and slip displacement

In this paper, an equivalent linearization method is applied. After some assumptions for the representation of the input displacement wave w and the slip displacement u using the relation u = w - v, the axial displacement and strain of the pipe can be determined.

The model of interaction between the pipeline and the surrounding soil presented in [6] by Todorov has four degrees of freedom. The first one refers to longitudinal pipe displacements. The second one shows the downward movement of the pipe. The third one represents the pipe movement along its horizontal axis, and the fourth one expresses uplift movements. Everyone of these four parameters has a different mathematical description for different soil conditions.

In [9], Mavridis and Pitilakis have developed an analytical procedure for calculating upper bounds for stresses and strains for transverse and axial loading cases of continuous buried pipelines, taking into account the soil-pipe interaction. Two models based on the Beam-on-Dynamic-Winkler-Foundation approach have been used for the calculation of both transverse and axial pipe displacements. It is assumed that the two directions may be examined independently.

Continuously distributed springs and dashpots are excited at their support by the free field displacements and they transmit the excitation further to the pipe, producing stresses and strains, Fig. 5. The seismic excitation is considered as a harmonic function of both time

and space thus defining a seismic S-wave traveling along the pipe axis. The pipeline is considered continuous, and the soil is assumed to be homogeneous, linear visco-elastic with material damping of frequency-independent hysteretic type.

Fig. 5 Lateral and axial response models

The governing equations of the pipe motion for transversal and axial directions are presented. Their solution is performed satisfying the boundary conditions. The solution expresses the relative displacement and the phase shift between pipe and soil. A detailed parameter study illustrates the influence of the apparent propagation wave velocity, pipe diameter and the frequency content of the seismic excitation on the ratio of the pipe to ground displacement amplitudes and consequently to the induced pipe strains.

Special attention is paid to papers [36 – 45] by researchers of the Banaras Hindu University in Varanasi, India. They have investigated the dynamic response of buried orthotropic cylindrical tick-shells subjected to P- , SH- and SV-waves, with an arbitrary incidence angle. The shell is assumed to be perfectly bounded in the surrounding linearly elastic, homogeneous and isotropic infinite medium (soil).

The equations of motion are expressed in terms of displacements. The tractions in the dynamic equations of the embedded shell are expressed completely in terms of the incident and the scattered field displacements in the surrounding infinite medium.

Effects of the shell orthotropy on its response have been illustrated by changing the non-dimensional orthotropy parameters of the shell over a wide range. The orthotropy parameters have been defined using the ratios of the deformation moduli in a cylindrical-polar coordinate system. It is found that the character and the degree of this influence vary in wide range depending on the specific combinations and other describing parameters (rigidity of the surrounding soil, propagation wave’s speed, wavelength, etc.) Results have been obtained for different soil conditions: hard (rocky), medium and soft soil.

Paper [42] deals with the non-axisymmetric dynamic response of an imperfect bonded orthotropic buried pipeline due to an incident shear wave. A thin layer between the pipe and the surrounding soil is assumed possessing both stiffness and damping properties. The degree of imperfection of the bond is varied by changing the stiffness and the damping parameter of this layer. It is concluded that in the non-axisymmetric mode, under certain conditions, consideration of bond imperfection may lead to an even higher value of pipe deformation than for perfectly bonded pipe.

Additionally to this model, in [37, 41, 43] the effect of stagnant fluid inside the pipeline has been accounted for. The linear acoustic equation has been used for the wave propagation in the fluid. It is observed that the effect of fluid presence is depending on the wavelength and speed of propagation of the incident wave and the soil conditions around the

pipe. The fluid inside a buried pipeline plays an important role affecting the dynamic response of the pipe. The effect of the fluid is more pronounced in softer soil and the influence of the fluid on the pipe response increases with increase of the ratio of the fluid density to that of the pipe. Effects of changes in the thickness to radius ratio of the shell have been discussed as well.

A comparison between the behaviour of thick and thin buried orthotropic cylindrical shells subjected to seismic excitation is presented, too. The thick and thin shell equations are discussed separately. The results show that the axial displacement of the shell may be significantly affected when the choice is changed from thick to thin shell approximation or vice versa. The magnitude of difference depends upon the ground conditions around the pipe, the wavelength and wave propagation velocities.

5. Fluid – Structure Interaction

Due to seismic shaking, additional hydrodynamic surge pressure in pipelines may be induced. There are some studies for evaluating of this earthquake-induced hydrodynamic pressure.

In [13], Nakagawa carried out theoretical studies on the effect of dynamic surge pressure and deduced a formula for calculation of the pressure increase in a pipe dead end during earthquake excitation. The hydraulic pressure effects on bends, tees and tapered pipe branches are related to the hydraulic dynamic pressure at a dead end.

The effect of hydrodynamic pressure in pipeline due to seismic excitation is studied in [10] by Wieland. In this paper, the hydrodynamic pressures in penstocks are governed by the one-dimensional wave equation and its solution is obtained with the mode superposition method. The input seismic excitation is specified by acceleration design response spectra [EC EN 1998-1:2004].

From the numerical examples solved in [10], conclusions may be drawn regarding the earthquake-induced hydrodynamic pressures:

• The hydrodynamic pressures in short penstocks can become quite high values during strong earthquake shaking. In this case, resonance-like pressure oscillations can develop, i.e. the lowest eigenfrequency of the pressure water-conveying system is in the range of the dominant frequencies of ground shaking. Thus, the assumption of an incompressible fluid leads to an underestimation of the hydrodynamic pressures.

• In penstocks with a length of several hundred meters and more, the lowest eigenfrequency of the pressure water-conveying system is far below the dominant frequencies of the ground motion. In this case, the maximum hydrodynamic pressures in a compressible fluid are below those of an incompressible fluid.

• The maximum hydrodynamic pressures depend on the shape of the acceleration response spectrum. In the case of long penstocks, the fundamental period of vibration is of the order of several seconds, which is beyond that of most buildings and bridges. Hence, the corresponding design spectrum values are rather low. Moreover, the design response spectra given in building codes may be rather inaccurate in that range of periods. Therefore, the design response spectra used for such analyses have to be reviewed carefully. This conclusion is in conformity with the well-known fact that the seismic response of this type of structures is controlled by the ground displacements rather than by the accelerations.

The papers [15, 16, 17, 18, 19] by Sv. Lilkova-Markova and V. Djupanov deal with the dynamic stability of short or long pipes conveying fluid and lying on elastic supports, or on elastic foundation. It is assumed that the pipe is homogeneous, isotropic and linearly

elastic and the fluid is non-compressible, inviscid and heavy. The fluid escaping from the free end of the pipe causes vibrations of the complicated three – dimensional mechanical system (flowing fluid – pipe – supports).

The case of high fluid flow velocity is studied when the reactive force at the free pipe end in combination with a small dynamic perturbation induces a complicated motion in the system. The motion amplitude can theoretically increase up to infinity, and the escaping fluid velocity in this case is the flutter critical velocity. The aim of the mentioned series of papers is evaluation of this flutter velocity for different models of the pipe and its supports.

The solution is performed using separation of the variables satisfying the boundary conditions. Parameter studies have been carried out as well, and the results are discussed in the mentioned works. However, this classical and quite complicated problem of dynamic stability of the fluid-conveying pipe in regard to the flow velocity is not directly related to the problem of earthquake-induced vibrations of a pipeline.

In [24], Kolic and Trifunac have studied the hydraulic transients in a dam bottom outlet during seismic excitation. It is assumed that the dam is rigid with vertical upstream slope, and the water in the reservoir and in the conduit is compressible. The analysis aims investigation of the influence of the hydrodynamic pressures due to the earthquake response of the dam and the reservoir bottom on generation of transient pressures along the bottom outlet as well as to demonstrate the possibility of using the method of Fourier transform in a hydraulic transient problem. The proposed numerical technique is implemented on a realistic bottom outlet model.

6. Conclusions

The carried out review of the currently accessible literature sources shows that the analysis of buried pipelines subjected to seismic excitation is a field of intensive research activities. There is a large number of research works, however, concentrated on different particular aspects of the problem. At the end of this review of the available theoretical models, some conclusions can be summarized as follows:

♦ The evaluation of seismic-induced hydrodynamic pressures in short or long water-conveying conduits has been elaborated for some system configurations. Quite limited number of models have been developed under strongly simplifying assumptions.

♦ The fluid – structure interaction is well studied in respect of the critical fluid velocity, relating to flutter oscillations, for different boundary conditions and supporting schemes. This model could not be applied directly in the case of seismic impact since there is no kinematic excitation applied to the supports.

♦ The extensive research work on the problem of soil – structure interaction has resulted in many well elaborated computational models covering all important complicated physical phenomena, including non-linear effects of imperfect bounding and slip between the pipe and the soil. There are lots of research works considering different type of seismic waves and different shell models for the pipe and surrounding soil characteristic data. However, some of these models are too sophisticated but in covering only some particular effects of the pipe – soil interaction.

To our best knowledge, there is currently no consistent computational model of buried pipeline subjected to seismic excitation, which even by means of some simplifying assumptions is able to uniformly cover all aspects of its seismic structural response.

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ИЗСЛЕДВАНЕ НА ЗАСИПАН НАПОРЕН ТРЪБОПРОВОД ПРИ ЗЕМЕТРЪСНО ВЪЗДЕЙСТВИЕ. СЪСТОЯНИЕ НА ПРОБЛЕМА.

I. МОДЕЛИРАНЕ НА ФИЗИЧЕСКИТЕ ЯВЛЕНИЯ И МЕТОДИ ЗА АНАЛИЗ

С. Петкова3, Д. Кисляков4

Ключови думи: засипан тръбопровод, сеизмично въздействие, взаимодействие тръбопровод – течност и тръбопровод – почва

Научна област: сеизмично инжeнерство, засипан тръбопровод

РЕЗЮМЕ

Настоящата статия представя първата част от систематичен преглед на основните групи изчислителни модели на засипан тръбопровод при сеизмично въздействие. От една страна целта на този анализ е да представи най-разпространените подходи за моделиране и изследване на поведението на засипан тръбопровод при земетръс и взаимодействията в системата почва-тръба-течност. От друга страна се цели установяването на пропуските в моделирането на сложното физическо взаимодествие свързано с динамичния отговор на засипаните тръбопроводи при сеизмично въздействие.

В първата част на извършения преглед вниманието е насочено към анализирането на характерните особености на групите изчислителни моделите. Представени са ключови параметри на моделите, чрез които се описват физическите явления, възникващи в сложната трикомпонентна система при сеизмично въздействие. В тази връзка са направени някои изводи по отношение на установените подходи, трудностите и отворените въпроси в процесите на моделиране и изледване на тези сложни динамични проблеми.

3 Силвия Петкова; маг. инж. докторант; катедра Хидротехника, УАСГ, бул. Хр. Смирненски 1, София 1046, България, e-mail: silvia _ petkova @ mail . bg

4 Димитър Кисляков, доц. д-р. инж.; катедра Хидротехника, УАСГ, бул. Хр. Смирненски 1, София 1046, България, e-mail: kiss _ fhe @ uacg . bg