Lateral interaction between pipelines and clays is governed by the rate of the interaction, overconsolidation and hydraulic conductivity of the clay, location of the groundwater table, and other factors. When the movement is slow enough and no excess pore water pressure generates, the soil response becomes drained. On the other hand, undrained soil response may occur when the movement is fast enough. For all other rates between these two boundaries, partial drained response of the soil occurs. Because overconsolidated clays have a quite different response in drained, undrained, and partial drained loading, different interaction forces are expected for the different interaction rates. The development of negative pore water pressure in the overconsolidated clay is an important factor in studying rate loading.
Altaee and Boivin (1995) performed finite element analysis of lateral pipeline-soil interaction. The clay considered was slightly overconsolidated and the effect of negative excess pore water pressure was not obvious. As most natural clays are highly overconsolidated in the zone of pipeline placement, extending the Altaee and Boivin (1995) analysis for highly overconsolidated clays is needed. Therefore, the present study addresses the effect of rate of movement, location of the groundwater table, soil’s overconsolidation, and suction developing behind rapidly moving pipelines on the lateral interaction force. The study employs a generalized coupled stress-consolidation analysis and therefore, the drained and undrained cases of analyses are only special cases.
In this paper, results of finite element analysis performed for a laterally displaced pipeline are presented. The pipe diameter and the size of trench were selected to represent full- scale conditions as documented by Rizkalla et al. (1993). The native soil and the backfill material were considered to be overconsolidated clays. The AGAC finite element program with the bounding-surface plasticity model for clays (Altaee, 1992) is used.
GEOMETRY ANALYZED
A sectional elevation of the geometry analyzed is shown in Fig. 1. The pipe is 914 mm diameter placed in a backfilled 2.0 m wide and 1.8 m deep excavation with 0.9 m of soil backfilled above the crown of the pipe. These dimensions are similar to those encountered in practice as pointed out by Rizkalla et al. (1992) and used by Altaee and Boivin (1995) and Paulin et al. (1995).
Altaee and Boivin (1995) performed finite element analysis to study lateral displacement of a pipeline by moving the soil laterally against the pipeline. In contrast, in the present analysis, the pipeline is moved laterally by imposing incremental lateral displacement on the pipe itself. This type of lateral interaction is commonly used in laboratory studies of pipeline soil interaction such as in Rizkalla et al. (1992) and Paulin et al. (1995). The resulting pipeline soil interaction caused by moving the pipeline against the soil rather than moving the soil against the pipeline is not necessarily fully representative to actual field conditions. However, it is selected in the present analysis for demonstrative purposes and to compare the analysis results to observations from laboratory testing.
FINITE ELEMENT PROGRAM AND SOIL MODEL
The Advanced Geotechnical Analysis Code (AGAC), Altaee (1992) is used to perform the present analyses. The program incorporates several constitutive soil models including the modified Cam-clay model, Cap models, and bounding surface plasticity models for cohesionless and cohesive soils. The program is fully operational on a PC Computer. Incremental-iterative procedures are used to deal with the non-linearity of the soil behavior.
All analyses performed in this study are generalized coupled stress-consolidation type and, therefore, ideal drained and ideal undrained situations become special cases of the generalized method of analysis used here.
The soil constitutive model has been successfully applied to heavily overconsolidated clays, which exhibit strain- softening and develop negative excess pore water pressure during shearing. Overconsolidated clays are very common in nature and particularly at shallow depths within the zone of interest for pipeline placement.
The bounding surface plasticity model for clays (Altaee, 1992) is used to simulate the behavior of the soil. A brief description of the model and its formulation is presented in Altaee and Boivin (1995).
FINITE ELEMENT MODEL
The finite element mesh used in the analysis is shown in Fig. 2. AGAC uses four-node isoparametric elements. The pipe is modeled as a linearly elastic material.
Vertical and horizontal movements as well as water flow are prevented along the boundaries AB, BC, and CD. No restriction on movement or water flow is imposed along Boundary DA. The flow from the soil into the pipe is prevented by specifying the outer surface of the pipeline as an impervious boundary. The boundaries AB, BC, and CD are placed far enough to eliminate any effect of the boundaries on the analysis results.
Interaction between the pipeline and soil is introduced by displacing the pipe laterally from left to right by applying increments of horizontal displacement as indicated in Fig. 2. Vertical movement of the pipe is not restricted.
CONCLUSIONS
When a pipeline is moved laterally against an overconsolidated clay, lateral interaction force develops. The faster the pipeline moves, the larger the resulting interaction force. For the clay considered in the present analysis, pipeline movement rate of 1 mm/day and 1,000 mm/day define the bounds of drained and undrained interaction, respectively. Any movement rate that is faster than 1,000 mm/day would not result in any further increase in the interaction force. Similarly, any movement rate that is slower than 1 mm/day would not result in any further reduction in the interaction force. These drained and undrained rates of movement depend on the hydraulic conductivity of the soil. The more permeable the soil, the faster the rate of pipeline movement needed to result in undrained interaction.
For all rates of pipeline movements, the higher the overconsolidation stress of the soil, the higher the resulting interaction force for the same lateral pipeline displacement. When the groundwater table is far below the pipeline, the resulting interaction force becomes independent of the rate of movement. For the same soil and pipeline, the interaction force when the soil is dry is larger than the interaction force of a slowly moving pipeline and smaller than the force of a rapidly moving pipeline when the ground water table is at the surface.
Negative excess pore water pressure develops behind a rapidly moving pipeline. The faster the rate of movement, the larger the resulting pore water pressure. When the negative pore water pressure is released fully from the soil behind the pipeline, the interaction force reduces to about half that when the pore water pressure is allowed to develop fully.
Under a moving pipeline, a zone of high shear strain develops. The faster the pipeline moves the larger this zone. In case of rapid movement, the zone extends to the ground surface in the soil behind the pipeline. Pipeline movement causes the soil to heave at the ground surface in a dome shape. The slower the movement the larger the dome. The formation of a depression at the ground surface is also observed when pipeline movement is rapid. This is due to the large suction developing behind the rapidly moving pipeline. When the suction is released, the ground depression does not develop.
The way the lateral interaction is introduced, the pipeline moves against the soil or the soil moves against the pipeline, affects the stresses, strains, and pore water pressure regimes and, therefore, the magnitude of lateral interaction force as a function of the rate of movement.
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