**2. Background**

The design of a suspended pipeline requires two alternative structure solutions: pipelines supported by auxiliary structures or self-supporting pipelines. In this research, a real case of auxiliary structures supporting a pipeline (*i.e.*, pipeline bridge) is studied. The preferred conceptual design of a pipe bridge consists of a straight configuration that can use a restrained mechanical joint ductile iron pipe (DIP) or a butt welded steel pipe with a pipe expansion joint, on a roller system, allowing the pipe to act independently of the superstructure [12]. This scenario is considered the ideal case because it is free of fittings and minimizes pipe joint deflections, which create thrust forces [13].

A stress analysis of the pipelines needs to be conducted to verify the integrity of the suspended structure, as the expected pressure extremes which ensure the applied pre-tension guaranteed that the columns remain in tension [14].

Many pipe failures in natural events have resulted from the sliding, rocking or overturning of large equipment to which the pipe is attached. During these events, the tanks may twist and slide in the concrete saddles, resulting in ruptures. It is therefore important to verify the adequacy of the anchorage equipment and tie-downs as part of design or retrofit of pipeline systems [15]. The same type of failure can take place when a pipe is connected to two separate structures (e.g., vertical pipe supports and lateral bracing).

The vibration caused by external or internal forces is transmitted to the pipe, and if the pipe is too stiff, this motion may cause the pipe to fail. Some building codes advocate the use of "flexible assemblies" to absorb differential building motion, such as placing a flexible assembly in the pipe where it crosses building joints [16]. However, most pipe spans are sufficient flexibles to absorb this differential movement. Otherwise, unless required by a building code, it is prudent to avoid placing these flexible assemblies at the preliminary design stage and only use them if there is no other alternative solution confirmed by detailed stress analysis [17].

In a suspended pipeline, this system can be idealized as continuous beams spanning lateral braces [18]. Commonly, vertical supports for gravity and operational loads are adequate to resist the vertical seismic forces, since the vertical component of seismic force is often lower than other vertical loads [19]. However, where a support resists to the vertical component of a lateral or longitudinal brace force, it should be designed explicitly to resist all applied forces, such as transient events.

### **3. Formulation of the Problem**

### *3.1. Description of the Accident*

Knowledge on the effect of a flowing mass on the dynamic response of suspended pipelines simultaneously under moving loads is still lacking from the point of view of structural design. The dynamic stability of suspension structures has been the focus of several studies [20–22]. However, few studies has been focused on the effect of interaction between fluid and structure, especially under different actions of the pipeline's suspension with pressurized flows. The purpose of this research is to investigate the dynamic effects involved in a suspended pipeline bridge by combining the maximum overloading and water-hammer phenomena.

The case study is based on an accident that happened in Ukraine 2005, where due to water-hammer phenomena the pipeline, used to transport oil to refineries, was set in motion, bent at the opposite ground entrance section *(i.e*., displacements in upper and transverse directions) and thrown from its supports. The measured pressures registered values higher than 10 MPa. This overpressure was responsible for the failure at an underground section, *i.e.*, 50 m from the surface section of the pipeline to the source (Figure 1).

**Figure 1.** Pipeline accident (adapted from [23]).

The material of the pipeline is steel and has a nominal diameter (ND) of 500 mm. The steel supports, fixed in concrete footings, have U-configuration with maximum spans of 15 m. After the water hammer phenomena, the pipeline moved about 1.50 m in the pipe direction (axis-*x*) and 0.75 m in the transverse direction (axis-*y*).

This accident highlights the importance of assessment of factors which cause instability and lead to eventual rupture, with analyses of the safety condition of strategic pipeline systems under pressure, mainly due to effects of water-hammer and earthquakes responsible for the rupture and fatigue of the structure. In the case of sudden changes (*i.e*., transient events, earthquakes), a pipeline's design rarely remains in good performance conditions. Thus, the vulnerability of the pipeline system to transient actions is analysed, through an advanced FEM structural analysis (Robot Autodesk), to simulate the consequences of a water-hammer in terms of displacements and loads in the pipes and support structures. Subsequently, comparisons are made between the results obtained at the accident and in simulations to better understand the causes and effects herein reported.

### *3.2. Definition of Physical Characteristics*

The system, based on the real case, is a pipeline with a total length of 74 m, composed of 6 steel supports with a 500 mm internal diameter (Figure 2). Three of the 6 supports are 3 m in height with a 15 m span, followed by 2 supports 1.20 m in height in the downstream section (Figure 2). The remaining upstream section has spans of 5 (*i.e.*, in the bend) and 7.4 m (*i.e*., in the initial section). The supports consist of 3 steel tubes with wall thickness of 50 mm. The pipeline is attached to two separate structures forming the supports. The pipeline has a thickness of 26.2 mm.

**Figure 2.** Pipeline system: part under analysis.

The chapters below present finite element results of the stresses and displacements in the pipeline and in supports due to internal pressure under the combination of the water-hammer event. Two combinations and nonlinear effects associated with each load are also studied separately. The material used for the pipeline, according to specifications ANSI/ASME B.31.4, is carbon steel API-5L Gr. B, with the characteristics presented in Table 1.


**Table 1.** Material specifications of the pipeline according to ANSI/ASME B.31.4.

Note: \* The maximum allowable stress accounts for the welding efficiency factor.

The selected material was estimated based on the maximum pressure achieved during the accident. Thus, Sch/serie 60 was chosen since the maximum allowable operating pressures is higher than that registered *in situ* and because the overpressure induced by the water-hammer did not cause the rupture of the pipeline.
