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.     

Analysis of buried pipelines subjected to reverse fault motion

Presently available simplified analytical methods and semi-empirical methods for the analysis of buried pipelines subjected to fault motion are suitable only for the strike-slip and the normal-slip type fault motions, and cannot be used for the reverse fault crossing case. A simple finite element model, which uses beam elements for the pipeline and discrete nonlinear springs for the soil, has been proposed to analyse buried pipeline subjected to reverse fault motion. The material nonlinearities associated with pipe-material and soil, and geometric nonlinearity associated with large deformations were incorporated in the analysis. Complex reverse fault motion was simulated using suitable constraints between pipe-nodes and ground ends of the soil spring. Results of the parametric study suggest that the pipeline's capacity to accommodate reverse fault offset can be increased significantly by choosing a near-parallel orientation in plan with respect to the fault line. Further improvement in the response of the pipeline is possible by adopting loose backfill, smooth and hard surface coating, and shallow burial depth in the fault crossing region. For normal or near normal orientations, pipeline is expected to fail due to beam buckling at very small fault offsets.     

Mitigation of reverse faulting deformation using a soil bentonite wall: Dimensional analysis,parametric study,design implications

Recent major seismic events, such as the Chi-Chi (1999) and the Wenchuan (2008) earthquakes occurred in Taiwan and China, have offered a variety of case histories on the performance of structures subjected to reverse faulting–induced deformation. A novel faulting mitigation method has recently been proposed, introducing a soft deformable wall barrier in order to divert the fault rupture away from the structure. This can be materialized by constructing a thick diaphragm-type soil bentonite wall (SBW) between the structure and the fault rupture path. The paper investigates the key parameters in designing such a SBW, aiming to mitigate the fault rupture hazard on shallow foundations. The paper employs a thoroughly validated finite element analysis methodology to explore the efficiency of a weak SBW barrier in protecting slab foundations from large tectonic deformation due to reverse faulting. A dimensional analysis is conducted in order to generalize the validity of the derived conclusions. The dimensionless formulation is then used to conduct a detailed parametric study, exploring the effect of SBW thickness w/H, depth H_SBWl/H, and shear strength τ_soil/τ_SBW, as well as the bedrock fault offset h/H, foundation surcharge load q/ρgB, and fault outcrop location s/B. It is shown that the wall thickness, depth, and shear strength should be designed on the basis of the magnitude of the bedrock fault offset, the location of the fault relative to the structure, and the shear strength of the soil. The efficiency of the weak barrier is improved using lower strength and stiffness material compared to the alluvium. A simplified preliminary design methodology is proposed, and presented in the form of a flowchart.     

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.     

Shaking table tests modelling small diameter pipes crossing a vertical fault

Local gas pipelines provide a valuable resource to urban areas and are often forced to cover unfavourable ground conditions in order to form a serviceable network. This can force pipelines through soil, which is subjected to permanent ground displacements due to faulting and strong vibrations due to earthquakes. Due to the inseparability of faulting from earthquakes it is pertinent to examine the combined effect of dynamic vibration and shear deformation of the surrounding soil on buried pipelines and a better understanding of the factors affecting pipe response to these inputs will enable more intelligent design of future pipe networks with the intention of reducing damage inflicted on pipes in extreme events. To advance understanding of this topic, a series of model experiments were performed under 1 g conditions on instrumented 20 mm diameter acrylic prototype pipes buried in dry Toyoura sand as well as a tyre derived aggregate (TDA) backfill trench surrounded by Toyoura sand crossing a vertical fault. The apparatus setup allowed faulting and dynamic input to be applied simultaneously to the model, which revealed that the simultaneous loading reduces the bending of a pipe and that installation of a pipe in a tyre derived aggregate backfill reduces the bending moment experienced by the pipe by up to 74% for small fault displacement and low levels of acceleration.     

Innovative mitigation method for buried pipelines crossing faults

A new remediation technique is proposed to mitigate large deformations imposed on buried pipeline systems subject to permanent ground deformation. With this technique, low-density gravel (LDG) with high porosity, such as pumice, is used as backfill in the trench containing the pipe near an area susceptible to PGD. This countermeasure decreases soil resistance, soil-pipe interaction forces and strain on the pipe as the pipeline deformation mechanism changes to a more desirable shape. Expanded polystyrene geofoam has been introduced to decrease the density of the pipeline backfill; however, LDG is more efficient regarding workability during construction, environmental effects, durability, fire safety, and cost-effectiveness. A series of centrifuge model experiments in which the pipelines were subjected to reverse faulting was conducted to evaluate the proposed method. During faulting, the axial and bending strain and pipe deflection were measured. A comparison of the responses of the remediated pipeline and the pipeline without remediation indicates that the proposed technique substantially mitigates the effects of large deformation.

     

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.     

Intensity measures for the assessment of the seismic response of buried steel pipelines

To estimate the demand of structures, investigating the correlation between engineering demand parameters and intensity measures (IMs) is of prime importance in performance-based earthquake engineering. In the present paper, the efficiency and sufficiency of some IMs for evaluating the seismic response of buried steel pipelines are investigated. Six buried pipe models with different diameter to thickness and burial depth to diameter ratios, and different soil properties are subjected to an ensemble of 30 far-field earthquake ground motion records. The records are scaled to several intensity levels and a number of incremental dynamic analyses are performed. The approach used in the analyses is finite element modeling. Pipes are modeled using shell elements while equivalent springs and dashpots are used for modeling the soil. Several ground motion intensity measures are used to investigate their efficiency and sufficiency in assessing the seismic demand and capacity of the buried steel pipelines in terms of engineering demand parameter measured by the peak axial compressive strain at the critical section of the pipe. Using the regression analysis, efficient and sufficient IMs are proposed for two groups of buried pipelines separately. The first one is a group of pipes buried in soils with low stiffness and the second one is those buried in soils with higher stiffness. It is concluded that for the first group of pipes, \(\sqrt {{\text{VSI}}[\upomega_{1} ({\text{PGD}} + {\text{RMS}}_{\text{d}} )]}\) followed by root mean square of displacement (RMS_d) are the optimal IMs based on both efficiency and sufficiency; and for the second group, the only optimal IM is PGD²/RMS_d.     

A simplified analysis model for determining the seismic response of buried steel pipes at strike-slip fault crossings

The seismic response analysis of buried pipelines at fault crossings is a complex problem requiring nonlinear 3D soil-structure and large deformation analyses. Such analyses are computationally expensive and the results are hard to evaluate. Therefore, a simple numerical model is needed for engineering and design offices to determine the seismic demand of steel pipes at fault crossings. This paper presents a simplified numerical model for buried steel pipes crossing strike-slip faults and oriented perpendicular to the fault. Two pipes with different diameter to thickness (D/t) ratios and steel grades are used in the study. The proposed model permits plastic hinge formations in the pipe due to incrementally applied fault movements, allows determination of the critical length of the pipeline and measure strains developed on the tension and compression sides in the pipe. The model also considers the effect of bending as well as axial strains due to stretching.     

Seismic simulation of liquefaction-induced uplift behavior of a hollow cylinder structure buried in shallow ground

When designing buried structures using a performance-based framework, it is important to estimate their uplift displacement. A simplified method is proposed for predicting the uplift displacement of a hollow cylinder structure buried in shallow backfill based on the equilibrium of vertical forces acting on the structure during earthquakes. However, this method only provides the maximum value, which frequently is overestimated in practical applications. To offset this limitation, first, the uplift behavior of buried hollow cylinder structures subjected to strong earthquake motions was simulated. Then, two-dimensional effective stress analyses based on the multiple shear mechanism for soil were conducted, and the results were compared with the centrifuge test data. The soil parameters were evaluated based on laboratory test results. The seismic response data from 20 g centrifuge tests were analyzed, and the results were generally consistent with the results of centrifuge model tests. In particular, the effective stress model showed a reasonable ability to reproduce the varying degrees of uplift displacement depending on the geotechnical conditions of trench soils adjacent to the hollow cylinder structures buried in shallow ground.     

A semi-analytical model for estimating seismic behavior of buried steel pipes at bend point under propagating waves

A buried pipe extends over long distances and passes through soils with different properties. In the event of an earthquake, the same pipe experiences a variable ground motion along its length. At bends, geometrically a more complicated problem exists where seismic waves propagating in a certain direction affect pipe before and after bend differently. Studying these different effects is the subject of this paper. Two variants for modeling of pipe, a beam model and a beam-shell hybrid model are examined. The surrounding soil is modeled with the conventional springs in both models. A suitable boundary condition is introduced at the ends of the system to simulate the far field. Effects of angle of incidence in the horizontal and vertical planes, angle of pipe bend, soil type, diameter to thickness ratio, and burial depth ratio on pipe strains at bend are examined thoroughly. It is concluded that extensional strains are highest at bends and these strains increase with the angle of incidence with the vertical axis. The pipe strains attain their peaks when pipe bend is around $135^{\circ }$ and exceed the elastic limit in certain cases especially in stiffer soils, but remain below the rupture limit. Then equations for predicting the seismic response of the buried pipe at bend are developed using the analytical data calculated above and regression analysis. It is shown that these semi-analytical equations predict the response with very good accuracy saving much time and effort.     

Underground pipeline response to earthquake-induced ground deformation

The principal causes of earthquake-induced ground deformation are identified and their interaction with underground infrastructure, primarily pipelines and conduits, is described. The coupled forces normal and parallel to underground pipelines arising from earthquake-induced ground movement are evaluated, including a review of measured stresses on pipe surfaces during large-scale testing, evaluation of frictional forces related to soil-pipe interaction, and the resolution of interaction forces along and across pipelines. Methods for characterizing soil reaction to pipe lateral and vertical movements are presented. The maximum downward pipe force is only about one-third the maximum force determined with conventional bearing capacity equations, thus requiring changes in current analytical and design practice. The analytical results for pipeline response to strike-slip and normal fault rupture are shown to compare favorably with the results of both large-scale and centrifuge tests of soil-pipeline interaction simulating these types of severe ground deformation.     

Centrifuge modeling of PGD response of buried pipe

A new centrifuge based method for determining the response of continuous buried pipe to PGD is presented. The physical characteristics of the RPI‘s 100 g-ton geotechnical centrifuge and the current lifeline experiment split-box are described: The split-box contains the model pipeline and surrounding soil and is manufactured such that half can be offset, in flight, simulating PGD. In addition, governing similitude relations which allow one to determine the physical characteristics, (diameter, wall thickness and material modulus of elasticity) of the model pipeline are presented. Finally, recorded strains induced in two buried pipes with prototype diameters of 0.63 m and 0.95 m (24 and 36 inch) subject to 0.6 and 2.0 meters (2 and 6 feet) of full scale fault offsets and presented and compared to corresponding FE results.     

Systematic deflection and offset of the Yangtze River drainage system along the strike-slip Ganzi-Yushu-Xianshuihe Fault Zone,Tibetan Plateau

The Ganzi-Yushu-Xianshuihe Fault Zone (GYXFZ) is a typical active strike-slip fault that has triggered many large historic earthquakes, including the 2010 M_w 6.9 Yushu earthquake in the central Tibetan Plateau. This fault zone extends for ca. 800 km from the central Tibetan Plateau to its southeastern margin and varies in trend from WNW-ESE in the northwestern segment of the fault zone to NNW-SSE in the southeastern segment, having the geometry of an arc projecting northeastwards. In this study, we present evidence for the systematical sinistral deflection and/or offset of the Yangtze River and its branch stream channels and valleys along the GYXFZ. Topographic analysis of three-dimensional (3D) perspective images constructed using digital elevation model (DEM) data, 0.5 m-resolution WorldView and GeoEye images, and 15 m-resolution Landsat-Enhanced Thematic Mapper (ETM+) images, together with analysis of geological structures, reveals the following: (i) the main river channels and valleys of the Yangtze River drainage system show systematic sinistral deflections and/or offsets along the GYXFZ; (ii) various amounts of sinistral offset have accumulated on the tributary stream channels, valleys, and gullies of the Yangtze River along the fault, with a linear relation, D = aL, between the upstream length L from the deflected point and the offset amount D with a certain coefficient a; (iii) the maximum amount of sinistral offset is up to ca. 60 km, which was accumulated in the past 13–5 Ma; and (iv) the long-term average strike-slip rate is ca. 4.6–12 mm/year. Geological and geomorphic evidence, combined with geophysical data, demonstrates that the GYXFZ is currently active as one of the major seismogenic faults in the Tibetan Plateau, dominated by left-lateral strike-slip motion. Our findings supply important evidence for the tectonic evolution of strike-slip faults in the Tibetan Plateau since the Eurasia-India continental collision.     

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.     

地震断层作用下的埋地管道等效分析模型

地震作用下,活动断层附近的埋地管道易发生强度屈服、局部屈曲或整体失稳等形式的破坏,建立准确、高效的埋地管道在断层作用下的计算模型,对管道的抗震设计和震后安全状态评估具有重要的实用价值。本文采用非线性弹簧模拟远离断层处埋地管道的反应,基于管土之间小变形段管道处于强化阶段,提出一种改进的管土等效分析模型,进一步减小了管土之间大变形段的分析长度,从而提高了有限元分析效率。该模型采用ALA推荐的方法计算管土间的滑动摩擦力,可以考虑土体种类的影响;用Kennedy方法确定管道的计算长度。通过与精确模型比较,验证了管土等效模型的合理性和有效性。     

跨断层水泥管试验的有限元分析

在考虑管道的材料非线性和几何非线性、管土相互作用的非线性和管道接口非线性的基础上,建立了由管体梁单元、三向土弹簧单元和接口单元组成的埋地非连续管道在断层位移作用下的有限元模型,并以美国密歇根大学Junhee等(2010)所做的跨断层水泥管试验为原型进行了模拟分析。有限元结果给出的水泥管最终变形、接口转角、接口位移与实验结果基本一致,表明本文提出的跨断层埋地非连续管道抗震计算的有限元分析方法具有一定的合理性。有限元结果和试验结果都表明,在逆冲断层作用下,水泥管的破坏主要是因为在管道接口处的轴向压力和弯矩的耦合作用,在断层附近的管道接口承受了较大的转动和压缩位移。本文所提出的分析方法可推广到埋地非连续管道在其它永久地面变形作用下的有限元分析。     

沉陷区域埋地管线数值模拟分析

场地的不均匀沉陷是导致埋地管线破坏的重要原因之一。本文考虑了材料非线性、几何非线性以及管土接触非线性,将管线计算分析模型模拟为四节点薄壳单元结构,周围填覆土体采用八节点六面体单元划分。管土相互作用模拟为三维刚性与柔性的面面接触单元结构,并采用线性位移加载来模拟土体的沉陷作用,对三维薄壳有限元模型进行数值计算分析。通过比较不同参数,如沉陷长度、沉陷深度、埋深、管径、径厚比、土特性等对管线的反应影响,得出管线在沉陷情况下的应力和应变的关系,通过算例分析,说明了该方法能更好地模拟管线的破坏过程,该方法将为沉陷区域埋地管线数值模拟提供理论分析依据。     

Uplift response of buried pipelines in saturated sand deposit under earthquake loading

Pipelines buried in saturated sand deposits, during earthquake loading could damage from resulting uplift due to excess pore water pressure generation. Several studies have been made to better understand the uplift mechanism and evaluate the effectiveness of mitigating techniques through experiment, but little numerical works have been done to assess the influence of soil properties and field conditions in pipeline floatation. Especially for previously buried pipelines, in order to set the priority for seismic retrofit, evaluating the risk of floatation in each region could be a concern. In this paper, effects of several parameters including dilatancy angle and density ratio of natural soil, diameter and burial depth of pipe, underground water table and thickness of the saturated soil layer on uplift of pipe have been investigated. Results show the prominent role of burial depth in pipe response and that there exits an optimum level for drop of water table to reduce floatation.     

Centrifuge modelling of normal fault–foundation interaction

Earthquake fault ruptures may emerge at the ground surface causing large differential movements. When fault ruptures emerge at or adjacent to the position of existing foundations, significant damage can be caused. However, the study of recent faulting events revealed that in some circumstances the fault-rupture emergence is deflected by the presence of buildings leaving the buildings intact. A centrifuge modelling study has been conducted to investigate how normal faults interact with strip foundations which run parallel to the strike direction. The study confirms that fault rupture may be deviated by the presence of the foundation so that the foundation is protected from the most serious differential movements. However, whilst the fault propagates to the soil surface the foundation has to withstand initial movements before the final fault rupture emergence mechanism is activated. The centrifuge results suggest that it is the bearing pressure of the foundation which causes the deviation of the fault rather than the kinematic restraint of the foundation. The interaction between the earthquake fault and the shallow foundation depends on the foundation bearing pressure, foundation width, soil depth and position of the fault relative to the foundation and these aspects should be considered in design. Results from the tests are used to validate a series of finite element analyses as reported in an accompanying paper.