Small Strain Finite Element Analyses Research Articles

Decoupled Analysis of a Multi-Layer Flexible Pipeline Buried in Clay Subjected to Large Lateral Soil Displacement

Multilayered flexible subsea pipelines may experience significant lateral movements due to manmade and environmental geohazards. These pipelines incorporate several structural and protective layers to resist different loads, and may require additional protection such as trenching, rock placement, or burial. In practice, simplifications are considered due to the complexities and uncertainties involved in the multi-layer pipe structure and the surrounding soil, compromising the pipe structure or the soil behavior. These simplifications are applied either on the pipe by assuming a rigid section or on the soil by representing it as elastic springs, which may result in inaccuracies. This study proposes a decoupled methodology combining the Coupled Eulerian–Lagrangian (CEL) model for soil displacement with a small-strain finite element analysis of the flexible pipe. This approach aims to accurately capture cross-sectional deformations and local stresses due to soil movement while maintaining reasonable computational effort. A parametric analysis was conducted to assess the impact of several variables on failure risk. The deformed cross-section was then used for a collapse analysis to determine critical loads at maximum operational depth. The study showed that modeling parameters such as soil strength and internal diameter might significantly influence pipe failure and the risk of collapse.

Uplift Behavior of Pipelines Buried at Various Depths in Spatially Varying Clayey Seabed

The behavior of buried offshore pipelines subjected to upheaval buckling has attracted much attention in recent years. Numerous researchers have made great efforts to investigate the influence of different soil cover depth ratios, soil strengths and pipe-soil interfaces on failure mechanisms and bearing capacities during pipeline uplift. However, attention to soil spatial variability has been relatively limited. To address this gap, a random small-strain finite element analysis has been conducted and reported in this paper to evaluate the influence of the random distribution of soil strength on pipe uplift response. The validity of the numerical model was verified by comparison with the results presented in the previous literature. The spatial variation of soil strength was simulated by a random field. The effect of soil variability on the failure mechanism was determined by comparing the displacement contours of each random realization. Probabilistic analyses were performed on the random uplift capacity obtained by a series of Monte Carlo simulations, and the relationship between the failure probability and the safety factor was also determined. The findings of the present work might serve as a reference for the safety designs of pipelines.

Soil failure mechanisms during installation and inclined pullout of stiffened suction caisson in calcareous silt

Soil failure mechanisms of stiffened suction caisson during installation and inclined pullout in calcareous silt have been investigated through centrifuge model tests and small strain finite element analyses (FEA). In the tests, a model half-caisson was installed followed by loading at a 45° inclination. Digital images were captured and subsequently analysed using particle image velocimetry (PIV), allowing soil failure mechanisms to be observed. The FEA were carried out to study the effects of pullout angles for caissons with and without internal suction. The PIV results revealed that during suction assisted installation, localised shear strains develop surrounding the skirt. As the stiffeners penetrated into the soil, the particles filled up the gaps between the inside wall and soil plug. During inclined pullout, a double wedge type failure was observed at the front and rear sides that extended to 1.5 caisson diameter at the soil surface. A pure shear type failure was observed around the skirt tip. The FEA results showed that, for caissons without internal suction, a wedge failure mechanism was prevalent. The size of the wedge decreased with increasing pullout angle. For caissons with internal suction, a rotational failure mechanism was apparent.

Generalized predictive framework for lateral break-out resistance of submarine pipelines considering nonlinear seabed geometry and consolidation

The ultimate capacity of submarine pipelines under combined vertical and horizontal loading, so-called lateral break-out resistance, is influenced by the change in seabed geometry due to the installation process and subsequent drainage with associated gain in soil shear strength due to consolidation. The majority of existing solutions in the literature and the current design practices for the assessment of lateral break-out resistance are based on small-strain geometry assumptions and the unconsolidated undrained soil response, i.e. without considering the change in seabed geometry due to installation or improvement in shear strength of the surrounding soil due to post-installation consolidation. In this paper, the effects of installation and subsequent consolidation on the combined load carrying capacity of on-bottom pipelines in a soft clay seabed are investigated and quantified in a systematic manner. A large deformation finite element approach coupled with the Modified Cam Clay plasticity model is adopted to simulate the installation of pipelines, and a series of coupled small strain finite element analyses are performed to study the consolidation and break-out response. A comprehensive range of normalised pipe installation depth, preload level and consolidation time period is considered. Results are interpreted using a critical state framework, and expressed in terms of generalized equations for ease of application in engineering design. A predictive methodology is developed for the estimation of combined load capacity of submarine pipelines in soft clay, including the influences of installation, drainage and consolidated strength.

A new expression to predict secant rotational stiffness of spudcan in undrained soils

The nonlinear behavior of spudcan foundation will lead to the decrease of the rotational stiffness of the spudcan, leading to the increase of the stress at the critical member of the offshore jack-up drilling platform. Secant rotational stiffness is used to represent the value of rotational stiffness of linear foundation model when the soil changes from elastic to elasto-plastic and then to plastic. In this paper, the “wished in-place” small strain finite element analysis (SSFE) analysis is used to simulate the load-displacement response of spudcans pre-embedded in the plastic soil, thus calculating the secant rotational stiffness of spudcans. New expressions of failure ratio and secant rotational stiffness are proposed with the coupling effect of horizontal force and moment taken into account.

Improving force resultant model for anchors in clays from large deformation finite element analysis

This paper presents an improved plasticity force-resultant model for anchors deeply embedded in clays, developed from large deformation finite element analyses. The current available force-resultant models for anchors are mainly developed from small strain finite element analysis while experimental approach has not been used due to technical challenges. The advantage of large deformation finite element analysis is that it provides much more data points to fit the yield surface than small strain finite element analysis, in addition to avoiding excess mesh distortion problems. Furthermore, the flow rule or normality can be effectively checked in the large deformation finite element analysis and further used to improve the fitting quality. After validated against retrospective simulations, the better performance of the developed plasticity force-resultant model is demonstrated by comparing with available experimental observations from centrifuge test.

Causes of post-installation penetration of jack-up spudcan foundations in clays.

This paper examines possible causes of additional spudcan settlement after preloading using both centrifuge model tests and small strain finite element analysis, in which spudcan settlement due to cavity collapse, consolidation settlement and settlement due to cyclic loading are incorporated. Back-analyses of seven jack-up rigs in the Gulf of Mexico show that even complete cavity collapse could only explain part of the measured additional settlements in the majority of the cases. Small strain finite element analyses also show that spudcan consolidation settlement is likely to account for even less of the additional settlement than cavity collapse in the sites considered. On the other hand, centrifuge model tests show that large amplitude cyclic rocking has a very significant effect on spudcan settlement, even if half of the preload has been removed. However, this effect cannot be explained by the exceedance of the yield envelope since the loading combination had not exceeded the yield envelope. One possible explanation is the stiffness and strength degradation of the soil under cyclic loading. In view of this, a conservative approach is recommended in instances where large amplitude cyclic rocking, such as that arising from storm loading, is expected shortly after preloading. The presence of lattice legs is found to reduce the spudcan settlement during large amplitude cyclic rocking.

Capacity of skirted foundations in sand-over-clay under combined V-H-M loading

Circular skirted foundations are used widely in the offshore oil and gas industry and renewable energy industry to support subsea infrastructure and founding turbines. The foundations are subjected to combined vertical-horizontal-moment (V-H-M) loadings during operation. This paper describes an extensive investigation of the response of installed circular skirted foundations under operational loadings in sand-over-clay. The overarching aim was to examine the influence of the presence of a sand layer on the combined load capacity. A detailed parametric study was undertaken through small strain finite element analyses, varying the thickness of the sand layer, embedment depth of the foundation (or skirt length), and level of vertical load mobilisation.The effect of the surface sand layer was profound for thicker sand layer of Ts/D > 0.2. Normalised failure envelopes were presented in v-h, v-m and h-m spaces. The FE results on the former two spaces showed unique trend, but not on the latter. New approximating expressions for describing the failure envelopes as a function of the sand layer thickness ratio, skirt length ratio and vertical load mobilisation level were proposed.

Elastoplastic consolidation above and beneath strip anchors under uplift forces

ABSTRACTAlthough the uplift behavior of offshore plate anchors under undrained conditions has been investigated well in the past, studies on the behavior of anchors under long-term sustained loading are in relatively few numbers. The time required for consolidation under sustained load is important because the shear strength of soil changes after dissipation of excess pore pressure. In this paper, small strain finite-element analyses have been performed to investigate the consolidation time history above and beneath strip anchors. The modified cam clay plasticity constitutive model is used for modeling coupled pore fluid stress analysis. The effects of magnitude of preloading with embedment level have been studied. As expected, the FE results have shown that excess pore pressure dissipation time for soil above the anchor increased with the increase in embedment depth and the magnitude of preload. Rapid dissipation of negative excess pore pressure beneath the anchor was observed with increasing embedment depth, if the preload magnitude is equal to or more than 60% of the undrained capacity. Observed consolidation responses are presented as nondimensional design charts and simplified equations for ease of practice.

Elastoplastic consolidation solutions for scaling from shallow penetrometers to pipelines

The build-up of friction on seabed pipelines is an important design consideration, affecting their stability and the resulting in-service strain and fatigue. The consolidation beneath a partially embedded pipeline has been investigated in the past and linked to the build-up of axial pipe–soil resistance. This paper extends previous work by providing solutions for consolidation around a new class of shallow penetrometer, to provide a basis to scale from site investigation results directly to the build-up of pipeline friction. Small-strain finite element analyses, using the Modified Cam Clay soil model, are presented for the novel toroid and ball penetrometers. The effects of initial penetrometer embedment, device roughness, strength gradient, and overload ratio have been explored in a comprehensive manner, and are compared with pipe results. The toroid penetrometer shows excellent agreement with an element of an infinitely long pipe, simplifying the scaling process. The ball penetrometer shows a faster consolidation response, typically by a factor of three, reflecting the more effective drainage mechanisms of a three-dimensional device compared to a plane strain device. The dissipation responses are fitted by simple equations to aid application in design.

Bearing capacity of rectangular footings in uniform clay with deep embedment

This letter is concerned with the undrained bearing capacity of rectangular footings with various aspect ratios and embedment ratios in uniform clay. It covers thin plate foundations with low aspect ratios and high embedment depth with embedment ratio up to 150. The work is based on small strain finite element analysis (FEA). After verification of the FEA model against existing solutions of the bearing capacity factors of rectangular footings, a series of FEA results are obtained. Based on the FEA results, a simple formulation is proposed to calculate the bearing capacity factor for rectangle footing with different aspect ratio in any embedment depth, extending the existing solutions to cover a wider ranges of footing aspect ratios and embedment ratios.

Generalized framework to predict undrained uplift capacity of buried offshore pipelines

Estimation of undrained uplift capacity is essential for the determination of optimal burial depth of buried offshore pipelines. However, a generalized prediction model that incorporates various factors influencing this capacity is scarce in the literature. In this paper, results from a series of small-strain finite element analyses are presented that explore the effects of pipe embedment, pipe–soil interface roughness, interface tensile capacity, soil shear strength, and unit weight on pipe uplift response. From the study, a simple method to predict the undrained upheaval resistance of buried pipelines for any practical range of pipeline and soil parameters is proposed. Factors associated with transition in failure mechanism with embedment are also examined. The numerical model is validated by comparing the results with available analytical and experimental data. Large-deformation finite element analyses have also been performed independently for a few cases to justify the applicability of small-strain methods in modelling pipe upheaval. Accuracy of the model for generalized shear strength profile is then examined by considering practical values of parameters over broad ranges. The proposed methodology gives results with maximum error less than 8% for all ranges of parameters and hence can be adopted in design practices.

A practical method to evaluate failure envelopes of shallow foundations considering soil strain softening and rate effects

This paper presents a practical method to evaluate the development of failure envelopes of coastal and offshore shallow foundations after the action of multi-directional cyclic loading considering soil degradation. This is realised by implementing a soil strain softening and rate model into a finite element package and using a combined approach of load controlled geometrically nonlinear finite element analysis and displacement controlled small strain finite element analysis. The gradual evolution of soil strain softening and rate effects are monitored and utilised to update the shear strength during the analysis under multi-directional cyclic loading. The failure envelope is then investigated based on the updated shear strength field of the soil. After introducing the approach and demonstrating with an example, a systematic study is presented to explore the effects of soil strain softening and rate parameters, soil stiffness index and period of cyclic loading on load carrying capacity of coastal and offshore shallow foundations. The results show that soil degradation should be taken into account in design of coastal and offshore shallow foundations because it is detrimental to the capacity of shallow foundations. Results of the parametric analyses have shown that soil sensitivity, relative ductility and the stiffness index have more influence on capacity of shallow foundations subjected to undrained cyclic preloading than strain rate parameter and the period of cyclic loading.

Failure Envelope Approach for Consolidated Undrained Capacity of Shallow Foundations

AbstractA generalized framework is applied to predict consolidated undrained VHM failure envelopes for surface circular and strip foundations. The failure envelopes for consolidated undrained conditions are shown to be scaled from those for unconsolidated undrained conditions by the uniaxial consolidated undrained capacities, which are predicted through a theoretical framework based on fundamental critical state soil mechanics. The framework is applied to results from small-strain finite-element analyses for a strip and circular foundation of selected foundation dimension and soil conditions, and the versatility of the framework is validated through a parametric study. The generalized theoretical framework enables consolidated undrained VHM failure envelopes to be determined for a practical range of foundation sizes and linearly increasing soil shear-strength profiles through the expressions presented in this paper.

Undrained bearing capacity factors for ring footings in heterogeneous soil

This paper examines the undrained vertical bearing capacity of a ring rough footing embedded in heterogeneous soil. Stability solutions for a wide range of geometric and material combinations are obtained by small-strain finite element analysis. Design tables and charts are provided for evaluating undrained bearing capacity factors as a function of the dimensionless parameters related to footing internal opening, embedment and soil strength heterogeneity. The results from the present analysis are compared with the experimental data and existing solutions reported in the literature. The transition from shallow to deep failure modes for the ring footing is broadly discussed in terms of the displacement pattern. The undrained bearing capacity factors for different values of soil friction angle are also studied to investigate the effect of friction angle on the undrained stability of ring footings in heterogeneous soil.

Consolidated undrained load-carrying capacity of subsea mudmats under combined loading in six degrees of freedom

A generalised framework is presented for predicting the consolidated undrained capacity of rectangular mat foundations on normally consolidated soft clay under combined loading in six degrees of freedom as a function of relative preload and degree of consolidation. Consolidated undrained response is investigated by coupled small-strain finite-element analysis using the modified Cam Clay plasticity constitutive model. Increases in the load-carrying capacity of a foundation under combined loading in six degrees of freedom following vertical preload with subsequent consolidation are demonstrated and quantified. The results are presented as failure envelopes in multi-directional load space and are shown to expand proportionally as a function of degree of consolidation for a given relative preload. A methodology and a set of expressions are provided to predict the shape and size of failure envelopes for rectangular mat foundations for any degree of preloading and consolidation.

Effect of load inclination on the undrained bearing capacity of surface spread footings above voids

Footings are often situated on ground that includes voids that were either undetected or had not formed at the time of construction. In this study, small-strain finite element analyses are conducted to investigate the influence of load inclination on the bearing capacity of surface spread footings on undrained homogeneous clay with single and double continuous voids. The numerical solutions are compared with existing theoretical and empirical predictions. The results are presented as failure envelopes expressed in terms of loads that are non-dimensionalised by the footing width and the undrained soil shear strength (these are known as bearing capacity factors) and loads that are normalized by the uniaxial ultimate load. If underground voids exist under the footing, the shape and the size of the failure envelope defining the undrained bearing capacity of the footing subjected to combined horizontal and vertical loading depends on the location, the geometry and the number of voids.

Undrained stability of surface strip footings above voids

This paper investigates the undrained vertical bearing capacity of surface strip footings on clay with single and dual continuous voids. Numerical solutions for a wide range of geometric and material combinations are obtained by small strain finite element analysis. Based on the results, design charts are provided for the calculation of the undrained bearing capacity factors as a function of the dimensionless parameters related to the vertical and horizontal void distances from the footing, void width and height, and spacing between the two voids as well as soil rigidity and non-homogeneity. In the footing-above-void system, the ultimate bearing capacity of the footing is governed by the three failure mode: roof, wall, and combined failure mechanisms.

A method for predicting the consolidated undrained bearing capacity of shallow foundations

The effect of consolidation on the undrained bearing capacity of both rough and smooth strip and circular surface foundations is investigated, examining the influence of the magnitude and duration of an applied preload and the initial over-consolidation ratio of the deposit. The investigation comprised small strain finite-element analysis, with the soil response represented by Modified Cam Clay. The results are distilled into dimensionless and generalised forms, from which simple trends emerge. Based on these results, a simple method for predicting the consolidated undrained bearing capacity is proposed.

Numerical modelling of seepage beneath skirted foundations subjected to vertical uplift

This study reports the results of small strain finite element analyses undertaken to determine the rate of displacement of skirted foundations subjected to uplift loading, due to combined swelling and seepage. Compatibility of foundation movement with cumulative seepage of water into the skirt compartment is modelled using a layer of soft poroelastic material immediately below the foundation top plate. Performance of the model is first assessed for a range of stiffness values for the soft layer. The model is then used to investigate the rate of displacement for skirt depths ranging from 0.1 to 1 times the foundation diameter. The results are compared with available theoretical solutions and experimental results, and expressions are provided for calculating the equivalent seepage lengths and resulting uplift velocities. The effect on the seepage behaviour of the presence of a gap down the external skirt–soil interface is also discussed.