CiSTUP Indian Institute of Science Bangalore

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1 EFFECT OF EMBEDMENT, PRELOAD AND CONSOLIDATION ON THE SERVICEABILITY AND BEARING CAPACITY OF SHALLOW EMBEDDED PIPELINES IN URBAN SPRAWL Final Report CiSTUP Indian Institute of Science Bangalore S.K. Valavala and T. G. Murthy Dept. of Civil Engineering Indian Institute of Science, Bangalore

2 Introduction Pipelines are a critical component in both onshore and offshore infrastructure projects, especially as the most important means of transportation of water, sewage, oil, hydrocarbons and many cases as a housing for electronic and communication channels. Pipelines that are either resting on the ground surface, or those which are embedded to shallow depths, are very frequently encountered in urban environs. Design considerations for these pipelines have very often been simplified to consideration of the pipe as a line load on the soil, largely ignoring servicebility of the pipeline. Servicebility challenges often encountered in pipelines can be broadly classified under buckling and walking (progressive axial displacement arising from cycles of expansion and contraction of the pipeline due to the temperature and pressure changes within the pipeline and its containing fluid, Carr et al 2006). These issues can be marginally controlled by using mechanical devices such as expansion joints and anchors, however such an alternative is quite expensive for both installation and maintenance (Perinet and Frazer 2006). So, an economic alternative would be to allow controlled buckling within the limits of strength and serviceability at the design stage of the pipeline (Bruton et al 2007). This report presents the highlights of a computational study which has been made on the behaviour of shallow embedded pipelines at small emdedments. Background Considering pipes of various diameters with varying ratios of embedment, Aubeny et al 2005 investigated the incerase in strength of the clay with change in soil strength profile. In this numerical study the authors infer a steady increase in the collapse load with increasing embedment of the pipeline. They draw upper and lower bound estimates of the collapse load for this problem with varying depths of embedment. In a more detailed study of the undrained resistance of partially embedded pipelines, Merifield et al 2008 present results of a detailed FE analysis with both horizontal and vertical loads applied to the pipeline. Yield envelopes with combinations of vertical (V) and horizontal (H) loading is (V-H) obtained from their research. Randolph and White (2008) propose upper bound yield envelopes for pipelines at shallow embedment in clay subjected to vertical and horizontal loads. In a recent study on the consolidation around partially embedded pipelines Krost et al 2011 study the effects of pore pressure dissipation and consolidation around pipelines. The curved 2

3 shape of the pipeline increased the rate of consolidation compared with a regular strip footing. The effect of embedment on the rate of consolidation was investigated in this paper. They also show that an overall increase in the axial resistance of the pipeline occurs due to consolidation, due to a wedging effect. Through controlled usage of the pipeline (i.e. by filling it to a fraction of its full capacity) and allowing for the consolidation of the clay (drainage at the surface) significant improvement of the bearing capacity can be achieved. This, also corresponds to the long term settlement of the pipeline, and the strength gain associated with it. Such a quantification exercise for seabed pipelines has already been made by Krost et al, This contact buit up between the pipeline and the clayey soil, can be compared to pile setup. (Krost et al 2011) The soil response to the laying of a pipeline at the short term can be regarded as undrained. With elapse of time, this excess pore pressure built up due to the undrained behaviour dissipates and the soil gains strength. The strength of the soil increases with depth and hence the bearing capacity of the soil increases with increasing embedment of the pipeline. The current study aims to quantify the concomitant effects of embedment, preload and consolidation on the bearing capacity of partially embedded pipelines. This study extends the study made by Krost et al 2011 for a pipeline that is partially embeded and examines the effect of long term strength gain due to consolidation around the pipeline. Finite Element Analysis (a) Geometry The finite element analyses was carried out with the commercially available finite-element software ABAQUS Version 6.11 (Dassault Systemes). Pipes of unit diameter embeded to different depths into a fine grained soil was modelled here. The pipe is considered to be rigid and no deflection of the pipe itself is allowed. The problem is analyzed under plane strain conditions, wherein length of the pipeline is considered to be much larger than its diameter. Pipeline embedment ratios depth of embedment to the diameter (d/d) = 0.1, 0.2, 0.3, 0.4 and 0.5 were considered in this analyses. The boundaries are placed sufficiently far away from the pipeline such that the boundaries have no effect on calculation of the ultimate bearing capacity and development of an ideal collapse mechanism is not hindered. The boundaries of the soil, are placed at about 20D on 3

4 either side of the pipeline, and about 10D underneath the pipeline, a Figure showing the schematic of the boundary condition is presented in Fig.1. (Additionally, the failure mechanism obtained from this analysis clearly shows no interaction with the boundary as inferable from Figure 13a). Fig. 1 Typical mesh for d/d = 0.1 showing the distribution of element density The pipeline is assumed to be a rigid body in this analysis, with rigid body elements used to model the pipeline. The rigid body elements are governed by a single reference point for defining all the displacement, loading and other boundary conditions that need to be applied to the clay (ABAQUS User s Manual). The soil (clay) is represented by linear strain quadrilateral pore pressure elements (library elements from ABAQUS CPE8RP), these elements have eight displacement nodes and four pore pressure nodes positioned at the corners of each element. A high density of elements is placed around the pipeline, which have an average size of about t=0.03d close the pipe-soil contact, in order to determine the shear stresses and strains with high precision; larger elements(with dimension t=1.45d) were placed in the soil mass away from the pipeline. A constant number of elements was not used in all the meshes, an optimum mesh size was obtained through a mesh sensitivity study. (b) Interface and Drainage Conditions 4

5 The interface between the pipeline and the soil is modelled to be rough so that slippage of the pipeline does not occur during loading; however no special interface elements were used in the simulations. The pipeline is assumed to be in contact with the soil at all times without any separation. A schematic of the FE model showing size and boundary conditions is presented in Fig. 2 The sides, base of the model and the pipe surface are all rendered impermeable and a drainage boundary is provided at the top surface to allow pore-pressure dissipation. The base of the model is fixed and the sides are restrained for displacement in the horizontal direction. B (or D) Drainage boundary 16B B 8B Fig. 2 Boundary Conditions used in the model (c) Soil Conditions The soil in the analysis is modeled with a Modified Cam Clay (MCC) constitutive model with shear strength linearly varying with depth. The saturated unit weight of the soil is 5

6 considered to be 17.18kN/m 3 and the soil is modeled with a surcharge on the top surface representing 1 m overburden. The shear strength profile of the soil is assumed to vary linearly with depth, as described Eq. 1 and presented in the schematic in Fig. 3 su = su0 + kz (1) where, s u0 is the undrained shear strength of the soil at the pipeline invert k is the gradient of the shear strength variation with depth. Fig. 3 A schematic of the geometry of the problem, indicating the presence of soil overburden, and shear strength profile with depth. Modified Cam Clay Model Application in ABAQUS The modified cam clay model (MCC) which is quite routinely used to model fine grained soils, is used in these simulations. A comprehensive description of the MCC model is not provided in this report, however a brief description of the MCC model and its implementation into Abaqus is provided below The modified Cam-Clay theory is an extension of the original Cam Clay formulation which effectively combines the idea of plastic flow or failure, which can be attained either through isotropic compression or shear stresses along with the attainment of a unique void ratio. The modified cam clay formulation is a slightly enhanced version of this idea. The MCC 6

7 fornulation here can be decomposed into an elastic and plastic part, the plastic part of the model is defined with a yield surface, a flow rule and a hardening rule which includes dilatancy (or volume change). The evolution of these quantities is controlled by the strain rate in the model. The numerical integration of the model is performed using backward Euler integration of the flow rule and the hardening rule. The elastic part of the model is based on a simple premise of poroelasticity, and is based on the experimental observation that in porous materials during elastic straining, the change in the void ratio e and the change in the logarithm of the mean stress p are linearly related, ( ln ( )) el de = κd p where, κ is the material parameter. In other words, the elastic part of the model follows the swelling line (or the unload-reload) line during an oedometer experiment on a soft clay. The MCC yield surface is defined by, (2) f ( p q r) p t,, = = β a Ma (3) Where, t is the deviatoric stress, M the slope of the critical state line, β and a are constants. a(θ,f α ) defines the hardening in the materia. An associated flow rule is used in the MCC model and the size of the yield surface is defined by a. The hardening or softening in the soil is controlled by the evolution of the parameter a The strain in the material, is computed from eq. 4 below ( ln ( )) de = λd p (4) The modified shape of the critical state line (from the regular Drucker Prager shape of a circle) is shown below in Fig. 3 7

8 Fig. 3 Modified shape of yield surface used for modelling MCC in ABAQUS (Ref: ABAQUS Version 6.11 User s Manual) Modified Cam Clay Parameters The parameters used for the model clay in the analyses are presented in Table.1. These are extracted from (Stewart 1992) 8

9 Table 1 Input parameters for the Modified Cam Clay Model extracted from Stewart (1992) Parameter input for analysis Magnitute 1. Parameters describing clay plasticity a. Log of Bulk Modulus (χ) b. Stress ratio at Critical State (M) c. Initial Yield Surface Size 0 d. Wet Yield Surface Size 1 e. Flow Stress Ratio 1 f. Intercept Parameters describing index and engineering properties of clay a. Mass density b. Permeability E-005 c. Void ratio Parameters describing elastic response (as a porous elastic material) a. Log of Bulk Modulus (κ) b. Poisson s ratio 0.25 c. Tensile limit 0 (d) Loading Each analysis regime in this research is carried out in 4 stages. The first stage consisted of creating the geostatic (equillibriation) stresses in the soil. This geostatic stresses in the soil ensures increase in stresses with depth. Subsequently, the excess pore water pressures was set up in the soil by applying the amount of preload to the footing (defined as a proportion of the undrained bearing capacity without preload) over a short period of time allowing no drainage. In the subsequent stage of the analysis, different periods of consolidation were permitted (total primary consolidation, T 100 ) and finally, a displacement was applied in the vertical direction on the center of the pipeline such that the soil would reach a state of continued plastic flow mechanism (or critical state). The reaction force provided by the soil is determined at the center of the footing. 1. Geostatic Step - The first step consisted of creating the geostatic stresses in the soil by providing self-weight and surcharge to the soil by considering the unit weight of the soil and the gravity load as a body force on the soil. Under equilibrium of stress conditions in the soil, a linearly varying shear strength profile of the clay is obtained. 9

10 For the case of no preload capacity or calculation of the ultimate undrained bearing capacity of the pipe embeded into clay. 2. Preload - A proportion of this ultimate undrained bearing capacity of the soil called preload - is applied at the reference point at the centre of the pipeline, for a short period of time without allowing any drainage; this sets up the pore pressures in the soil. 3. Consolidation In the subsequent step, once the pore pressures are set up due to the application of a preload, the soil is allowed to consolidate, i.e. dissipation of the excess pore pressure by permitting drainage of the pore water through the drainage boundary provided at the free surface of the soil (excluding the pipe which is considered impermeable). The pore pressures generated is allowed to dissipate completely in order to achieve a 100% primary consolidation. 4. Loading - Finally, a vertical displacement is applied to the reference point of the pipeline such that the soil would reach a state of continued plastic flow (or critical state). The diplacement is applied sufficiently quickly such that no pore pressure dissipation maybe permitted during this step, thus obtaining the undrained shear strength of the soil. The reaction force provided by the soil is determined at the reference point of the pipeline. Assessment of Stresses and Bearing Capacity Factor The ultimate bearing capacity (q) of the soil is calculated from the reaction force (RF) that the soil provides to the movement of the rigid pipeline. In order to obtain the bearing pressure, the distribution of the reaction force over the length of contact of the pipeline with the clay is considered. The bearing capacity factor, N c, is calculated from eq. 5 considering appropriate correction factors for depth, shape, inclination and strength non-homogeneity. q= F d i s s N c c c u0 c (5) S u0 is the shear strength of the soil in line with the pipeline invert, the shear strength of the clay from the MCC model is calculated as per the procedure outliend by Potts and Zdravkovic (2000). The depth factor (d c ) shape (s c ) and inclination (i c ) factors are obtained from Salgado (2008); and strength non-homogeneity factor (F) from Gourvenec et al (2003). The factors considered are provided below (eq.6-eq.10) 10

11 ' D Depth factor, d c d (6) c = B Where, D is the depth of the pipeline invert and; B is the effective width of the footing (in contact with the soil) Q Inclination factor, i c i h (7) c = Q v Qh is the stress in the horizontal direction and; Qv, the stress in the vertical direction B Shape factor, s c s (8) c = + L F κ 2 3 Factor for strength non-homogeneity, F = 1+ a (9) 1κ+ a2κ + a3κ F 0 ( ) ( ) kb where, κ is the degree of non-homogeneity, κ = (10) s Calculation of the undrained shear strength of the clay from MCC is given below, s u0 u0 NC 2 su 1+ 2K0 1+ B 2 = g ( θ) cosθ 2 σ B v κ λ (11) where, σ v is the stress in the vertical direction, K 0 NC - co-efficicent at rest for the normally consolidated clay given by, NC K0 = 1 sinφ cs (12) Critical state friction angle, ϕ 3M cs; sinφcs = 6 + M (13) M is the critical state stress ratio i.e. the slope of the critical state line in stress space (in the q- p space) 11

12 g ( θ ) sinφcs = 1 cosθ + sinθsinφcs 3 (14) g(θ) is a mathematical function that defines the shape of the plastic potential surface, θ being the Lode angle (θ = for Tri-axial compression θ = 0 for plane strain condition) NC ( K0 ) 31 B = g ( 30) K NC 0 (15) Benchmarking The accuracy and precision of the mesh, along with the boundary conditions imposed was assessed using a standard case of a shallow strip footing founded on a soft clay. The analyses was carried out for the case of a normally consolidated clay. The bearing capacity factor N c assessed from this FE simulation was compared to analytical / semi-analytical solutions available from method of characteristics and numerical limit analysis (i.e. for a rough footing soil interface and with no surcharge the bearing capacity factor is (2+π) (Salgado 2008). Mesh Sensitivity Study Convergence of the FE analyses is sensitive to the characteristics of the mesh used, additionlly, the time required for analyses also is dependent on the characteristics of the FE mesh. A mesh sensitivity study was carried out in order to accurately assess the optimum number of elements for the analysis which would satisfy criteria of both accuracy and time of analyses. Meshes with different density of elements was used and the analyses was performed, the bearing capacity factor was computed, along with the time taken for each of these analyses. The bearing capacity factors obtained from the analyses are presented in Table 2. Increase in the mesh density (i.e. number of elements) resulted in a better prediction for the Nc value i.e. 12

13 higher accuracy, based on which the number of elements in the mesh were optimised for the different embedment ratios. No. of elements Nc N c, analytical = 5.14 Results A FE study has been made here to understand the effect of embedment and preloading on a pipeline bearing on a soft normally consolidated clayey soil. The ultimate undrained vertical capacity of the clay, while the pipeline was placed on the surface of the clay was first estimated and is designated as Vult. Effects of embedment depth and preload applications are outlined here. 1. Effect of Embedment Embedment of the pipeline into the surface of the clay is examined in this simulation, The embedment ratios of d/d = 0.1 to d/d = 0.5 are simulated here. The vertical load carrying capacity increases with increase in the embedment depth of the pipeline; and there is a 95% increase in the bearing capacity from with a 5 time increase in embedment. Figure 5 shows the load versus normalised displacement (normalised with respect to diameter of the pipe) for pipelines at different embedment depths. The load carrying capacity of the soil is calculated from the resistance force (RF) on the pipeline ; 13

14 Figure 5 Load vs normalised displacement curves for pipelines with different embedment depths; inset shows the increasing trend of the normalised load, V max /s u0 D, with increasing embedment depth. The load normalised with the undrained shear strength of the soil at the level of the pipeline invert, s u0 and the width of the footing, which is the diameter of the pipeline, D - V max /s u0 D - increases with embedment of the pipeline as shown in the plot inset in figure 5. The bearing capacity factor, N c is calculated from the reaction force on the pipeline at the reference point (RP),. From figure 6, it is observed that the value of N c decreases with increase in embedment depth. 14

15 Figure 6 Bearing Capacity Factor, N c for pipeline at different embedment ratios 2. Effect of Preloading Fractions of the ultimate load bearing capacity, ranging from 10% to 70%, were applied as preload on the soil at the reference point of the pipe and the soil was allowed to consolidate. The consolidation was allowed till all the pore pressure was dissipated from the soil ensemble. The consolidation hardens the soil but also brings forth settlement in the soil, and the improvement in the strength due to this consolidation is estimated by applying an additional vertical displacement to the pipeline until failure. Figure 7 presents the load versus displacement during the loading stage after complete primary consolidation under different preloads on the pipeline with embedment ratio, d/d = 0.3. Almost a 50% increase in the bearing capacity of the soil is seen with application of a 70% preload. 15

16 Figure 7 Increase in the vertical capacity of a normally consolidated soil, with the application of various magnitudes of preload for a pipeline embedment ratio d/d = 0.3 Figure 8 shows the increase in the normalised bearing capacity load of the soil with increasing preload for various depths of embedment. The increase in depth of embedment does not change the trend or the slope of the curves. About 20% gain in the bearing capacity was increased immaterial of the depth of embedment. Figure 8 Increase in the normalised bearing force, V max /s u D with preloading 16

17 3. Consolidation Fractions of the ultimate load was applied to the pipeline as a preload, and the soil was allowed to consolidate for a time elapse sufficient enough so that all the excess pore water pressure built up due to the application of preload. The extent of consolidation is presented as a displacement vs. time elapse in days. At the end of consolidation, the displacement of the pipeline equilibrates to a constant value and correspondingly, the pore pressure values at the nodes of the soil elements are almost equal to zero (a tolerance of around 10-3 kpa is deemed acceptable). The time required for complete primary consolidation is around 10 5 days, and the displacement time cures are presented for the case of an embedment depth ratio of 0.1 for various values of preloads is presented in Figure 9(a). Figure 9(a) Time histories of consolidation settlement under different preloads on a pipeline at an embedment ratio, d/d = 0.1 From the time histories of normalised settlement due to consolidation; i.e. the ratio of settlement at any time, t, to the settlement after primary consolidation (w f ) of the footing as shown in figure 9(b), it can be observed that the plots collapse into one trajectory, with minor differences in the rate of consolidation. 17

18 Figure 9(b) Time histories of normalised consolidation settlement for consolidation under different preloads on pipeline at embedment ratio, d/d = 0.1 A similar normalized time history of settlement, with increasing d/d is shown in Figure 10. The plot indicates that the consolidation is faster for pipelines at lower embedment depths. Figure 10 Time histories of normalised consolidation settlement 18

19 Figure 11 shows time histories of excess pore pressure dissipation at the pipe invert for each of the pipe embedment ratios during consolidation under a 70% preload. The excess pore pressures are normalised by the initial excess pore pressure immediately after application of the load, u i ; and time shown is in logarithmic scale. Krost et al (2011) report similar behaviour and explain it by the Mandel Cryer effect a stress transfer phenomenon in which the dissipation process creates a local rise in total stress, leading to an increase rather than a decrease in excess pore pressure (Mandel, 1950; Cryer, 1963) which is evident for all embedment depths; but as the consolidation process stabilizes it is observed that the rate of dissipation of excess pore water pressure is faster for lower embedment depths and becomes slower with an increase in the embedment depth. Figure 11 Time histories of normalised excess pore water pressure dissipation 4. Comparison of Bearing Capacity with existing studies: The values of the bearing capacity normalised with the diameter of the pipeline and the undrained shear strength of soil obtained from the current study are compared with those obtained from previous studies. The current study estimates a higher bearing capacity over the estimates from previous studies. 19

20 Figure 12 Comparison of the increase in normalised bearing capacity, V max /s u D from the current study with existing data 5. Displacement Fields: Typical displacement fields obtained at failure for an embedment ratio (d/d=0.3) is shown in Fig. 13a, the figure shows a quiver plot showing the direction of traverse of the soil, with application of an axial load to the pipeline. The displacement field is similar in general feature to a strip footing resting on a normally consolidated clayey soil. A region of velocity right at the invert region shows an almost vertical direction with a magnitude equal to the pipe displacement, akin to a dead wedge seen in a strip footing. 20

21 Figure 13 (a) The displacement field at failure obtained from ABAQUS, for embedment ratio, d/d=0.3 Fig. 13b shows the displacment field obtained from the FE analysis and a upper bound displacement field (from Merifield et al 2008) used to calculate the upper bound limit load, qualitatively confirming the accuracy of the analyses. Figure 13 (b) Comparison of displacement fields at failure obtained from analyses to the failure envelope from upper-bound solution, for d/d =

22 Conclusion Finite element analyses has been used to investigate the improvement of the vertical bearing capacity of a pipeline founded on a soft clayey soil, with application of a long term vertical loads. These vertical loads can be envisioned as partial service of the pipeline (fractional filling of the pipeline) over long times to allow consolidation of the clay. Due to this consolidation, an increase in the bearing capacity is seen over long time periods which increases with the magnitude of preload The effect of the depth of embedment of the pipeline is also investigated in this research, with higher depths of embedment showing a substantial increase in the bearing capacity With these findings from the FE analysis, it maybe concluded that a sufficient emebedment would not only anchor the pipeline, but would also increase the bearing capacity of the clay pipeline system. Additionally, in designing the pipeline for long service periods, the long term loading, which causes settlement of the underlying clay needs to be considered. It is conservative to ignore consolidation strengthening in design, however, this may lead to a non optimal design solution. 22

23 NOMENCLATURE D Width of the footing/ Diameter of the pipeline D Depth of the pipeline invert B Effective width of the footing d Embedment depth of the pipeline N c Bearing Capacity Factor PP/u Excess pore pressure dissipated from the soil from the boundary layer at the free surface at any time instant, t PP i /u i Excess pore pressure developed in the soil at the instant immediately after loading s u Undrained shear strength of the soil s u0 Undrained shear strength of the soil at invert of the pipe V max Maximum vertical force per unit length of pipe w Displacement of the pipeline reference point at a time t w f Final displacement of the pipeline reference point at failure 23

24 REFERENCES: 1.) Aubeny, C. P., Shi, H. & Murff, J. D. (2005). Collapse load for cylinder embedded in trench in cohesive soil. Int. J. Geomech. 5, No. 4, ) Bruton, D., Carr, M. & White, D. J. (2007). The influence of pipe-soil interaction on lateral buckling and walking of pipelines: the SAFEBUCK JIP. Proc. 6th Int. Conf. Offshore Site Investigation Geotech., London, ) Carr, M., Sinclair, F. & Bruton, D. (2006). Pipeline walking understanding the field layout challenges, and analytical solutions developed for the SAFEBUCK JIP. Proceedings of the offshore technology conference, Houston, Texas, USA, Paper OTC ) Dassault Systemes. (2011). ABAQUS Users Manual, Version Providence Rhode Island. USA. 5.) Gourvenec, S. & Randolph, M. (2003). Effect of strength non-homogeneity on the shape of failure envelopes for combined loading of strip and circular foundations on clay. Geotechnique 53, No. 6, ) Hill, A. J. & Jacob, H. (2008). In-situ measurement of pipe-soil interaction in deep water. Proceedings of the offshore technology conference, Houston, Texas, USA, Paper OTC ) Krost, K., Gourvenec, S.M. & White, D. J. (2011). Consolidation around partially embedded seabed pipelines. Geotechnique 61, No. 2, ) Merifield, R., White, D. J. & Randolph, M. F. (2008). The ultimate undrained resistance of partially embedded pipelines. Geotechnique 58, No. 6, ) Murff, J. D., Wagner, D. A. & Randolph, M. F. (1989). Pipe penetration in cohesive soil. Geotechnique 39, No. 2, ) Perinet, D. & Frazer, I. (2006). Mitigation methods for deep water pipeline instability induced by temperature and pressure. Proceedings of the offshore technology conference, Houston, Texas, USA, Paper OTC ) Potts,D.M., Zdravkovic, L. (1999). Finite element analysis in geotechnical engineering: Theory. London: Thomas Telford. 24