Numerical Investigation of the Effect of Recent Load History on the Behaviour of Steel Piles under Horizontal Loading K. Abdel-Rahman Dr.-Ing., Institute of Soil Mechanics, Foundation Engineering and Waterpower Engineering Leibniz University of Hannover, Germany M. Achmus Prof. Dr.-Ing., Institute of Soil Mechanics, Foundation Engineering and Waterpower Engineering Leibniz University of Hannover, Germany Keywords: Numerical modelling, Offshore piles, Recent load history, Lateral loading. ABSTRACT: In this paper the effect of a change in the lateral load direction on the overall response of laterally loaded foundation piles in sand is investigated. A three dimensional numerical model using the finite element program Abaqus was developed. In this model the material behaviour of the subsoil is described using an elastoplastic constitutive model. The behaviour of a nearly rigid and of a flexible pile under lateral loading is investigated, taking a lateral preloading in a different direction into account. It is found that the preload can significantly affect the pile behaviour. Due to recent load history, the pile stiffness increases. The quantity of this increase is dependent on the angle between the directions of preload and current load and on the magnitude of the preload in relation to the current load. 1 Introduction Although foundation piles exhibit optimum performance under axial loads, in many cases also lateral loads have to be transferred to the subsoil. This is in particular valid for offshore piles, since offshore foundation structures have to withstand large wave and wind forces. These horizontal loads of course act in varying directions and thus the behaviour of piles under lateral (horizontal) loads with varying directions is of interest. An offshore foundation structure for which particularly large horizontal loads occur is the monopile foundation of offshore wind energy converters. Several offshore wind farms have been erected recently in the North Sea and the Baltic Sea, and most of the converters were founded on monopiles. A monopile is a large diameter steel pipe pile which in principle is a prolongation of the tower shaft into the ground. A schematic drawing of such a foundation is shown in Fig. 1. In water depths between about 10 and 20 m the required diameters vary between about 3.5 and 5 m. In the German sea regions wind farms are planned at water depths larger than 30 m up to 50 m. In these depths, for instance jacket structures can be used as foundations. These are steel lattice structures, which are supported by piles of smaller diameter (max. about 3.0 m) in the edges of the jacket. These piles are loaded mainly in axial direction, but again also in varying horizontal directions. In the current design of piles the variation of the horizontal load direction is not considered. However, it is to be expected that preloading in a different direction affects the behaviour of a foundation pile under the current load. The phenomenon recent load history (recently investigated by Levy et al. 2007) implies that the behaviour of such piles is dependent on previous loading events as well as on the currently applied loading. This paper aims to investigate the behaviour of vertical piles in sand soil subject to changes in horizontal loading direction.
Figure 1. Monopile Foundation (schematic). 2 Problem definition The system investigated here is shown in Fig. 2. A steel pipe pile with outer diameter D and thickness t embedded in medium dense sand with length L is considered. The load consists of a constant vertical force and a horizontal force with varying direction. First, a horizontal load is applied as a preload (initial loading). After unloading, only elastic deformations are recovered. Due to the elasto-plastic behaviour of soil, a plastic deformation remains after loading and unloading and the stresses in the soil around the pile differ from the initial stress state. This affects the behaviour of the pile under reloading. Reloading is applied in a different direction, described by an angle θ to the initial load direction (see Fig. 2). Due to the recent load history, the resultant displacement Δu under this load is in general not purely in θ-direction. The component of the displacement in θ- direction is denominated Δu θ. Cross section H V Ground view on pile head Sand L H u res Δu θ Δu t θ H Initial loading Unloading Reloading D Figure 2. System definition and denominations. The development of the resultant pile head displacement u res and of the differential displacement Δu θ with horizontal loading is the main subject of this investigation. Two cases are considered: a pile with a diameter of 2 m and an embedded length of 30 m and a pile with a diameter of 3 m and an embedded length of 20 m (Table 1).
Table 1: The pile dimensions and their rigidity. Case Diameter (D) Length (L) Wall thickness (t) Elastic length (L e ) L/L e Class 1 3.0 m 20.0 m 0.04 m 5.63 m 3.55 stiff 2 2.0 m 30.0 m 0.04 m 4.40 m 6.80 flexible A general classification of the behaviour of laterally loaded piles can be obtained by the ratio of the elastic length L e and the actual embedded length L. The elastic length relates the pile and the soil stiffnesses and can be derived from models in which the soil reaction is idealized by elastic springs (subgrade reaction models). For sandy soils a linear increase of the spring stiffnesses with depth z under the soil surface is a common approach: K s = k r z, with k r in MN/m 3. With this approach, the elastic length is defined as follows: E.I p p L 5 e = (1) kr Herein E p I p is the bending stiffness of the pile. For medium dense sand, a typical value for k r is k r = 15 MN/m 3. Using this value, the L/L e -values given in Table 1 apply for the two cases considered. With these values the pile of case 1 can be classified as a stiff and the pile of case 2 as a flexible pile. This means that for case 2 bending deformation of the pile prevails, whereas for case 1 the deformation is due to both bending and rigid body rotation. 3 Numerical Modelling To investigate the behaviour of piles under horizontal load in different directions, 3-D finite element calculations with the program system ABAQUS (2006) have been performed. In order to carry out the calculations for different loading conditions, an advanced computer system with parallel processor technology was used to minimize the computation time. The discretized model area was extended by six times the pile diameter in the radial direction, whereby the bottom boundary of the model was extended by four times the pile diameter beneath the base of the pile (Fig. 3). With these model dimensions the calculated behaviour of the pile is not influenced by the boundaries. For the soil as well as for the pile continuum elements were used. The frictional behaviour in the boundary surface between the pile and soil was modelled by contact elements based on slave-master-concept, whereby the friction angle was set to δ = 0.67 ϕ. The material behaviour of the steel piles was assumed to be linear elastic with the parameters E = 2.1 10 5 MN/m 2 (Young s modulus) and ν = 0.2 (Poisson s ratio). Appropriate modelling of the material behaviour of the soil plays an important role for the quality of the numerical computation of soil structure interaction problems. The elasto-plastic material law with Mohr-Coulomb failure criterion, provided in ABAQUS, was used. This material law was extended in the elastic range by introducing a stress-dependent oedometric modulus of elasticity described by the following equation: λ σ κ σ σ m = at at E S (2) Herein σ at = 100 kn/m 2 is a reference stress and σ m is the current mean principle stress in the regarded soil element. The parameter κ determines the soil stiffness at the reference stress state and the parameter λ rules the stress dependency of the soil stiffness. This material law has the advantage that it can be generally used for both cohesive and non-cohesive soils. The material parameters for medium dense sand used here are given in Table 2.
Table 2. Material parameters used in the numerical computations. Material Unit weight Stiffness Poisson s Shear parameters γ in kn/m 3 κ in 1 λ in 1 ratio ν φ in c in kn/m 2 ψ in in 1 Sand, medium dense 11 400 0.60 0.25 35 0.1 5 Figure 3. A view of the finite element mesh (only one halve of the soil is shown). The calculations were carried out stepwise in different stages. In the first calculation stage the initial stress condition for homogeneous sandy soil was generated (geostatic step). Subsequently, the pile was generated by replacing the soil elements located at the pile position by steel elements and activating the contact conditions between the pile and soil. Afterwards the vertical load was applied for the consideration of the own weight of the superstructure. In both cases 1 and 2 a vertical load of V = 3 MN was applied and kept constant during the following stages. Three further phases were defined in the context of these investigations. In the fourth phase a horizontal load of H = 8 MN (case 1), and of H = 15 MN (case 2), respectively, was applied in the 1-direction (see Fig. 3, direction 0 ) at the soil surface level. Subsequently, the pile was unloaded (5 th Phase). Then it was finally loaded in another horizontal direction with a certain angle to the 1-axis (6 th phase). Different angles (θ) ranging from 0.0 to 90.0 were examined. 4 Numerical Results The results are presented in terms of the horizontal load and the respective pile head displacement. Loaddisplacement curves for the stiff pile (case 1) are presented in Fig. 4. The pile was preloaded by a horizontal force H = 8 MN. Reloading was simulated in different directions between 0 and 90 to a maximum load of H = 16 MN. The development of the resulting displacement (with regard to the initial unloaded state) is depicted in Fig. 4, left. It is found that the initial inclination of the reloading curves is the larger, the larger the angle θ is. With θ = 90 almost a decrease of the resultant displacement during the begin of preloading is obtained. This means that the pile head initially moves along a way with constant or even decreasing distance to the location of the pile head before preloading.
15 15 H in MN H in MN 10 Reloading 10 angle θ 0 5 30 45 5 60 Reloading angle θ 0 30 45 60 90 90 Monotonic 0 0 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 u res in cm Δu θ in cm Figure 4. Load-displacement curves for different load direction angles (case 1: D = 3 m, L = 20 m). The initial state with regard to reloading is the displaced pile head after preloading. The stiffness or the deformation behaviour for reloading is then characterized by the differential displacement Δu θ in the direction of reloading (see Fig. 2). In Fig. 4, right, the reloading load-deformation curves are given. The stiffest pile behaviour is obtained for reloading in the same direction as the preloading (θ = 0 ). However, also for θ = 90, i.e. reloading perpendicular to the initial load, the pile behaves stiffer than for monotonic loading. This means that recent load history or preloading has a favourable effect on pile behaviour. Similar results were obtained by Levy et al. (2007) using a single yield surface model for piles in soft clay. To take a deeper look in the results in terms of stiffness, a system secant stiffness k sec is defined as follows: H k sec = Δu θ This value normalized by the initial stiffness of the monotonic loading curve is given in Fig. 5 dependent on the normalized differential displacement in reloading direction. Here the significant increase of stiffness due to recent load history can be seen very clearly. It is also evident that the stiffness increase gets smaller, when the displacement and the applied load become larger. If the reloading force is equal to the preloading force, i.e. here H = 8 MN, the secant stiffness increase lies between 25% for θ = 90 and about 45% for θ = 0. However, if the current load is much higher than the preload, the stiffness differences are small and can be neglected. sec init, mono k / k 1,0 0,5 Reloading angle θ 0 60 30 90 45 Monotonic 0 0 0,02 0,04 0,06 0,08 0,10 Δu θ / D in 1 Figure 5. Normalized secant stiffness versus normalized displacement (case 1: D = 3 m, L = 20 m).
The reason for the increased stiffness with reloading is of course a densification of the soil around the pile during first loading. Also, the different behaviour during initial loading and reloading can be explained on the basis of the mobilized horizontal stresses developed in the subsoil as shown in Figure 6. Under the first loading condition, horizontal passive stress σ 11 will be mobilized in the front of the pile, while a loosened zone or even a gap may develop in the region behind the pile. After removal of this loading, the stress state condition in the soil will be different from the initial stress state, possibly also with a gap between the pile and the surrounding soil. By reloading in 90 -direction the gap will close, first, and horizontal stresses in the 2-direction σ 22 will be gradually mobilized and increased. The change of the initial stress state due to the preloading leads to an increase of the overall stiffness of the pile-soil-system. σ x bzw. S11 Loading 0 σ x bzw. S11 Unloading σ x bzw. S11 Reloading 9 0 σ y bzw. S 22 Loading 0 σ y bzw. S22 Unloading σ y bzw. S22 Reloading 9 0 Figure 6. Mobilized horizontal stresses in medium dense sand (Case 1: D = 3,0 m, L = 20,0 m) (Forgoso 2007). The load-displacement curves for the flexible pile (case 2) are presented in Fig. 7. The pile was preloaded by a horizontal force H = 15 MN. Reloading was simulated in different directions between 0 and 90 to a maximum load of H = 25 MN. The results are very similar to the case 1 results. Also a stiffer behaviour with reloading compared with monotonic loading is observed. If the reload is equal to the first load (H = 15 MN), the stiffness increase is about 40% for θ = 0 and still about 10% for θ = 90. The initial decrease of the resultant displacement for θ = 90 is even more pronounced than for the case 1 pile. In Fig. 8 the normalized initial stiffness versus the normalized displacement is also given for the flexible pile of case 2. Again it is found that preloading leads to a significant stiffness increase, if the preload was in the same range or even higher than the current load. Vice versa, if the preload was small compared to the current load, the stiffness increase is also small.
H in MN 25 25 20 20 H in MN 15 Reloading 15 angle θ 10 0 10 30 5 45 60 5 Reloading angle θ 0 30 45 60 90 0 90 0 Monotonic 0 25 50 75 100 0 25 50 75 100 u res in cm Δu θ in cm Figure 7. Load-displacement curves for different load direction angles (case 2: D = 2 m, L = 30 m). sec init, mono k / k 1,0 0,5 0 Reloading angle θ 0 60 30 90 45 Monotonic 0 0,02 0,04 0,06 0,08 0,10 0,20 0,30 Δu θ / D in 1 Figure 8. Normalized secant stiffness versus normalized displacement (case 2: D = 2 m, L = 30 m). 5 Conclusions In this paper the results of a numerical study regarding the influence of recent load history with respect to horizontal loading of piles in sand are presented. It is proved that there is a significant influence. A pile which was subject to preloading behaves stiffer than a pile without preloading. The quantity of the stiffness increase depends on the magnitude of the preloading force in relation to the actual force and is the higher, the more the directions of initial loading and reloading coincide. However, also for a load acting perpendicular to the preload a stiffness increase arises. In future, the favourable effects of recent load history should be taken into account in the design of piles under horizontal loading in varying directions. However, for the development of a practical design approach much more research and in particular a thorough parametric study on the most important parameters is necessary. 6 References ABAQUS 2006. User Manual, Version 6.6.
Abdel-Rahman, K. & Achmus, M., Finite Element Modelling of horizontally loaded Monopile Foundations for Offshore Wind Energy Converters in Germany, International Symposium on Frontiers in Offshore Geotechnics (ISFOG), Perth, Australia, 2005. Forgoso Lara, P : Numerische Modellierung von Pfählen unter horizontaler Belastung mit verschiedenen Einwirkungsrichtungen, Master Thesis, IGBE, Leibniz Universität Hannover (unpublished), 2007. Levy, N.H., Einav, I. & Randolph, M.F. : Effect of recent load history on Laterally loaded piles in normally consolidated clay, International Journal of Geomechanics, ASCE,7(4), 2007. The paper may be considered for (Please indicate your choice by putting in the appropriate box) 1. Oral Presentation 2. Poster Session