Modelling of upheaval buckling of offshore pipeline buried in clay soil using genetic programming
Introduction
In the last few decades, the operating temperatures and pressures for subsea oil and gas pipelines have dramatically increased due to the deep sea explorations. This causes axial thermal expansion in pipeline; however, the expansion is resisted by soil friction that will set up the axial compressive force in the pipe wall. The compressive forces are frequently large enough to induce either lateral buckling in as-laid pipe or upheaval buckling in buried pipe. Moreover, the new trend towards using small diameter pipes has potentially increased the risk of buckling in accordance with the greater axial loads. Although these two buckling modes (i.e., lateral or upheaval) are not essentially failure modes, they can precipitate failure through excessive bending. This may cause fracture, fatigue or propagative buckling [12], [3].
Prediction of upheaval buckling resistance of buried pipelines has been a challenge as a result of uncertainty in the behaviour of seabed and cover soils, operating condition and pipe material [26]. The design and assessment of offshore pipeline against upheaval buckling are mostly based on the early analytical work reported in Randolph and Houlsby [23] and Maltby and Calladine [15]. Several experimental works were also reported in the past [27], [5], [4], [8], [16] to understand the uplift resistant provided by soil cover to pipe buried in granular soils. However, very limited number of studies was reported in the literature for pipe buried in clayey soils. Recently, Cheuk et al. [7] and Thusyanthan et al. [26] reported the experimental work to understand the uplift resistance of clay. However, the effect of variability in soil properties in uplift resistance has not been quantified, which requires significantly high number of experiments. One of the feasible ways to quantify the effect of variability in soil properties and other parameters is to model the pipeline system numerically and simulate the possible scenarios.
In this paper, upheaval buckling behaviour of offshore pipeline buried in clayey soils has been investigated numerically. Possible variability in soil uplift resistance, operating condition and pipe properties has been considered in the analysis. To simulate the upheaval buckling behaviour, a 2-D finite element model of 500 m long pipeline-seabed system was developed in OpenSEES [17]. The uncertain variables were modelled using appropriate probability distributions discussed in Rajeev et al. [21], and also the optimised Latin Hyper Cube (LHC) sampling technique was utilised to draw the sample for numerical simulation. Finally, genetic programming was used to develop the upheaval buckling predictive equations with varying accuracy and complexity. The effect of uncertain in soil and pipe material properties and operating conditions in the upheaval buckling response of buried offshore pipeline was also quantified. The developed upheaval buckling height predictive equations can be used to improve the design and risk assessment of pipeline against upheaval buckling.
Section snippets
Definition of the problem
A 500 m of offshore pipeline was considered for the analysis with the pipe material properties given in Table 1. The OpenSEES (finite element software) was employed to model pipe-seabed soil system and to conduct the thermal analysis. In this study, the pipe was modelled with elastic beam element using displacement based beam–column element with steel thermal properties, while the seabed and cover soils were modelled with elastic zero-length spring element. The fibre section was used to model
Probabilistic modelling of uncertain variables
The soil cover, operating condition and pipe material and geometric properties are treated as uncertain variables that have significant influence in the performance of pipeline. Following variables are considered: elastic modulus of backfill soil (Es), pipe wall thickness (t), pipe elastic modulus (Ep), operational temperature (T) and pressure (P), product density (γp). The assigned probability distribution and its statistical properties of considered variables are listed in Table 1 that gives
Modelling procedure by genetic programming
Genetic programming (GP), which was proposed by Koza [14], is one of the newest paradigms of evolutionary computations and is capable to automatically learn the introduced problem through mimicking Darwinian evolution process [6]. An extension to GP is gene expression programming (GEP) that was used in this paper to develop the upheaval buckling predictive models. GEP is able to create computer programs, which can be written in MATLAB or C++, of different sizes and shapes encoded in linear
Results and discussion
The expression trees were obtained for all the GEP predictive models proposed in this study. A sample of these ETs obtained for GEP9 model is shown in Fig. 3. In this figure, d0, d1, d2, d3, d4 and d5 denote to thickness (t), elastic modulus (EP), clay stiffness (ES), temperature (T), pressure (P) and product density (ρ) respectively. The constants c0 and c1 are produced during training of an ET, and are different in each sub ETs. Equations of all 12 proposed GEP models (simplified and by
Conclusions
In this paper, the genetic programming was used to develop predictive models for upheaval buckling height of offshore pipeline buried in clayey soil. The models were developed using the finite element simulation data. The simulation was carried out by considering the variability in pipe geometric properties and material behaviour, soil stiffness and pipe operational conditions. On the basis of the simulated data, 12 predictive models that are different in terms of number of genes, linking
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