Influence of pullout loads on the lateral response of pile foundation

Influence of pullout loads on the lateral response of pile foundation Mahmoud N. Hussien & Mourad Karray Department of Civil Engineering, Sherbrooke University (QC), Canada Tetsuo Tobita & Susumu Iai Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan ABSTRACT The influence of both compression and pullout loads on the lateral response of vertical piles installed in sandy soil is studied through two-dimensional finite elements. The interaction between the pile and the surrounding soil in threedimensional type was idealized in the two-dimensional analysis using soil-pile interaction springs with hysteretic nonlinear load displacement relationships. Soil models were idealized by multiple shear mechanism of hyperbolic type. Joint elements with separation-contact mechanism were used to idealize the separation effect at the soil-pile interface. Unlike the compression vertical loads that tend to increase the lateral capacity of a vertical pile installed sandy soil, numerical results show that pullout loads generally decrease the ultimate lateral capacity of piles. The increase or decrease in the confining pressures in the sand deposit at shallow depths is the major driving factor to contribute the increase or decrease in the lateral resistance of piles, depending on the direction of the applied vertical load. RÉSUMÉ L'influence de deux types de chargement, compression et arrachement, sur la réponse latérale de pieux verticaux installés dans un sol sablonneux est étudiée par éléments finis en deux dimensions. L'interaction entre le pieu et le sol environnant dans les trois dimensions a été idéalisé dans l'analyse en deux dimensions en utilisant des ressorts d'interaction sol-pieu avec des relations charge-déplacement hystérétique non-linéaire. Les sols ont été idéalisés par un mécanisme de cisaillement multiple de type hyperbolique. Les éléments communs avec mécanisme contact-séparation ont été utilisés pour idéaliser l'effet de séparation à l'interface sol-pieu. Contrairement aux charges verticales en compression qui tendent à augmenter la capacité latérale d'une pile verticale installé un sol sablonneux, les résultats numériques montrent que les charges d'arrachement diminuent généralement la capacité latérale ultime des pieux. L'augmentation ou la diminution de la pression de confinement dans le dépôt de sable à faible profondeur, est le facteur majeur qui contribue à l'augmentation ou la diminution de la résistance latérale de pieux, en fonction du sens de la charge verticale appliquée. 1 INTRODUCTION Pile foundations have been used for many years as common foundation solutions for offshore structures. Offshore structures are in general subjected to a combination of lateral loads and overturning moments due to wind loads, wave pressures, earth pressures, and ship impacts. The overturning moments are transferred to the structure foundations in the form of compression axial forces on some piles and pullout forces on others. Although it is obvious that the presence of these axial forces may affect the lateral carrying capacities of piles, all traditional methods of pile analysis consider that axial and lateral loads to act independently, and the interaction between these loads was not significant (Hussien et al. 2014). In the conventional methods of pile analysis, soil is modelled by spring elements attached to the pile at different depths. These springs generally have nonlinear load-displacement characterizations called (t-z) and (p-y) curves for axial and lateral loading, respectively. These two types of springs are generally uncoupled and therefore soil reactions along the corresponding degrees of freedom are also uncoupled. In other word, the influence of load acting in one direction on the characteristics of the spring in the other direction is neglected. However, recent studies based on finite element analyses of single piles (i.e. Karthigeyan and Ramakrishna (2006) and Karthigeyan et al. (2007), and Hussien et al. (2012), (2014)) suggested a significant increase in the lateral resistance of piles in the presence of vertical loads. In fact, the scopes of these recent studies were limited to the behavior of single piles subjected to compressive vertical loads. Yet, little work has been devoted to the behavior of piles subjected to the combined action of pullout axial and lateral loads. In this study, the influence of compression and pullout loads on the lateral capacities of vertical piles installed in sandy soil is studied through two-dimensional (2D) finite elements (FE) analyses. The interaction between the pile and the surrounding soil in three-dimensional (3D) type was idealized in the 2D analysis using soil-pile interaction springs with hysteretic non-linear load displacement relationships. Soil models were idealized by multiple shear mechanism of hyperbolic type, FLIP (Iai et al. 1992). Joint elements with separation-contact mechanism are used to idealize the separation effect at the soil-pile interface (Hussien et al. 2010). Initial results from this study are presented and the primary findings were summarized as conclusions. 2 FINITE ELEMENT MODELING AND MATERIAL PROPRTIES 2.1 Finite elements The 2D FE program FLIP was employed to analyze the behavior of piles under pure lateral loads and a

combination of vertical (compression and pullout) and lateral loads. Figure 1 shows the general layout and meshing of the FE model. Side boundary displacements were fixed in the horizontal direction, while those at the Pile diameter D = 324 mm Vertical loading direction bottom boundary were fixed in both the horizontal and vertical directions. The top and bottom of the pile were set as displacement and rotation free. Lateral loading direction Embedded depth 11.6 m 18 m 60 m Figure 1. General layout and meshing of the FE model. 2.2 Soil model The soil model used in this study consists of a multiple shear mechanism (Iai et al. 1992). The model is formulated based on the concept of contact forces in granular media. In this model, contact forces between soil particles are idealized by evenly distributed multiple springs, whose property is characterized by a non-linear load-deformation relationship. The multiple shear mechanism soil model is now widely used in design practice, especially for designing geotechnical structures in port and harbors in Japan. In the analysis, a uniform layer of sand is used. Model parameters of sand are shown in Table 1. 2.3 Pile model A steel pipe pile has a 0.324 m outside diameter with a 9.5 mm wall thickness and an embedment depth of 11.6 m is used. The lateral load was applied 495 mm above the ground surface. Bilinear beam elements are used for modeling piles. Model parameters of pile elements are defined in Table 2 (Tobita et al. 2006). 2.4 Soil-pile interface Joint elements are used at the soil-pile interface to represent sliding mechanism between them. Figure 2 indicates that sliding will be initiated when the shear stress at the interface exceeds a certain value of τ f given by the equation: f cj tan J [1] where c J and J are shear strength parameters of soil at the interface. Model parameters for joints element are defined in Table 3. 2.5 End bearing spring The axial soil reaction at pile tip is simulated using nonlinear spring element (Q-Z curve). The nonlinear spring at pile tip is represented according to Zhang et al. (1999) as: Q (1 υ) z b [2] Q 4r G (1 b ma ) o Q f where Q f = ultimate tip resistance (force); G ma and = initial shear modulus and Passion s ratio of the soil at the pile tip, respectively; r o = pile radius; and Q b = mobilized tip resistance (force) for the given displacement z. Table 1. Model parameters of sand elements. Soil layer sat (t/m 3 ) ma G ma K a f (degrees) Sand 1.83 98 4.35 10 4 0.33 1.14 10 5 33 G ma: initial shear modulus at a confining pressure of ma; ma: reference confining pressure; f: internal friction angle; : Poisson s ratio; K a: the bulk modulus of the soil skeleton. Table 2. Model parameters of pile elements. Gs A EI 0 EI 1 M p (t/m 3 ) (kn m) 77,500,000 0.29 7.9 0.03 109,000 10,900 875 G s: shear modulus; : Poisson s ratio; ρ: density; A: cross section area/unit width; EI 0: initial flexural rigidity; EI 2: flexural rigidity after yield; plastic bending moment. Table 3. Model parameters for joint elements. Angle of friction ( J) Normal stiffness Kn (kn/m 3 ) Tangential stiffness Ks (kn/m 3 ) 2/3 f 1,000,000 1,000,000 2.6 Soil-pile interaction spring Nonlinear-spring elements as shown in Fig. 1 are used to model the interaction between the pile and the

surrounding soil in horizontal direction. Parameters of the spring element were determined by parametric studies on soil-pile interaction in 2D horizontal plane as shown in Figure 3. Figure 3(a) shows a single row of equally spaced piles deployed perpendicular to the direction of load and Figure 3(b) shows a simplified model for one pile in the group. Figure 4 shows the load-relative displacement relationship of soil-pile system in the simplified model of one pile in the group under cyclic loading. As a part of the analysis of soil-pile system in horizontal plane, a simulation of shear stress-shear strain relationship of a single soil element under cyclic loading is performed and presented in Fig. 5. The relationship between load and relative displacement of a pile (Fig. 4) and the relationship between shear stress and shear strain of one element of the soil (Fig. 5) are similar to each other. Based on this similarity, the relationship between the relative displacement of a pile and the shear strain in an element test of soil as well as the relationship between the spring force and the shear stress in the soil element can be calibrated calibrated. More details about soil-pile interaction springs can be found in Ozutsumi, et al. (2003)). Figure 2. Sliding mechanisms at soil-pile interface Figure 3. 2D analysis of soil-pile system in horizontal plane. Figure 5. Simulation of shear stress-shear strain relationship of a single soil element. 3 RESULTS AND DISCUSSION A total of 3 cases were considered. A pure lateral load is considered in the first case while a combination of vertical and lateral loads is considered in the other two cases. In the latter two cases, a vertical displacement (V) of 0.1D (D = pile diameter) was applied at the pile head either compression in one case or tension (pullout) in the other case prior to the application of the lateral load. Lateral loads are then statically applied until a target lateral displacement of 60 mm is achieved. The maximum vertical displacement at the pile head was kept constant during the application of the lateral displacement. Results of the analyses on pile response under both lateral and combined loads, shown in Figure 6, indicate that a vertical load inducing a vertical displacement (V = 0.1D compression) of the pile head leads to an 8 % increase in the lateral load-carrying capacity of the pile at a lateral deflection of 60 mm. On the other hand, a vertical displacement (V = 0.1D tension) leads to a 4 % decrease in the lateral load-carrying capacity of the pile at the same lateral deflection. Similar percentages of increase or decrease depending on the direction of the applied vertical load were induced in the maximum shear force and bending moment in the pile as shown in Figs. 7 and 8. Load (kn) Figure 6. Load-deflection curves of the pile. Figure 4. Load-relative displacement relationship of the soil-pile system in the simplified model. Figure 9 shows the variation of horizontal soil stresses of soil elements along the depth of the pile before and after the application of lateral loads for the analyses with

and without vertical compression loads. In particular, the soil stress at the back side of the pile was plotted in Fig. 9(a), whereas that at the front side was plotted in Fig. 9(b). Moreover, horizontal soil stress profiles induced before and after the application of vertical compression loads were introduced for comparison purposes. These figures show that the inclusion of vertical compression loads prior to lateral loads increases the horizontal stress of soil elements along the depth of the pile not only at the front side but also at back side of the pile. The enhanced soil reaction is counterbalanced to some extent by a loss of a horizontal soil stress that occurs in the region approximately 6D above the pile tip. This is due to the interaction of the pile base movement and of the soil just above the pile base elevation. Figure 9 also indicates that the effect of vertical comp loads on the induced horizontal soil stresses lasts even after the application of lateral loads. Figure 7. Shear force profile of the pile. Figure 8. Bending moment profile of the pile. Figure 9. Horizontal soil stresses along the depth of the pile at before and after the application of vertical compression and lateral loads: back side (left); front side (right).

Similarly an attempt to identify the mechanism of the increase or decrease in the lateral resistance of a single pile subject to a vertical compression or tension load was made by studying deformation and stress changes induced in soil due to the applied vertical load. Figure 10 shows the variation of horizontal stresses of soil elements along the depth of the pile after the application of lateral loads for the analyses with and without vertical loads. In particular, the soil stress adjacent to the back side of the pile was plotted in the left side of the Fig. 10 whereas that adjacent to the front side was plotted in the right of the figure. Figure 10 shows that the inclusion of a vertical compressive load prior to the lateral load leads to an increase in the horizontal stress of soil while the inclusion of a tension load leads to a decrease in soil stress not only at front side but also at the back side of the pile. Figure 10. Horizontal soil stresses along the depth of the pile at different loading stages and conditions: back side (left); front side (right). The heave and downdrag of the soil by the vertical loaded pile as it moves up and down are shown in Figs. 11(a) and 11(b), respectively. In these figures, displacement field was scaled by 20 times relative to that of the geometric scale. Figure 11(a), corresponding to vertical pile loaded by vertical compressive load, shows that soil near the ground surface rotates due to the action of the vertical load on the pile head and the center of rotation is located just below the ground surface and at some distance from the pile. As a result of this rotation, in the vicinity of the pile, the displacement vectors of soil at shallow depths (up to 10D) are directed towards the pile whereas those at deeper depths are directed away from the pile. The resulting lateral displacement of soil at shallow depths pushes the soil toward the pile, inducing an increase in the lateral stress σ ) x) in the soil leading to an increase in the subsequent lateral capacity of the pile. Figure 11(b), corresponding to vertical pile loaded by vertical pullout load, shows opposite trend with the center of rotation is located approximately at the same horizontal distance from the pile but at a deeper depth. CONCLUSIONS been studied in this paper through two-dimensional finite element analyses. The interaction between the pile and the surrounding soil in three-dimensional type was idealized in the two-dimensional analysis using a soil-pile interaction spring with a hysteretic non-linear load displacement relationship. The primary findings from this study are summarized as follows: 1. The influence of vertical compression load is to increase the confining pressure in the sand deposit surrounding the pile, leading to an increase in the lateral pile resistance. A vertical compression load applied to a single pile with a vertical displacement of 0.1 pile diameter (D = 324 mm) leads to an 8 % increase in the lateral pile resistance at a 60 mm lateral deflection. 2. The influence of vertical tension load is to decrease the confining pressure in the sand deposit surrounding the pile, leading to a decrease in the lateral pile resistance. A vertical tension load applied to a single pile with the same vertical displacement leads to a 4 % decrease in the lateral pile resistance at the same lateral deflection. The effect of compression and pullout vertical loads on the lateral response of piles embedded in sandy soil has

(a) (b) Figure 11. Soil displacement field due to vertical load on the pile head: (a) compression; (b) pullout. REFERENCES Hussien M.N., Tobita T., Iai S., Rollins, K.M. 2012. Vertical load effect on the lateral pile group resistance in sand response. An International Journal of Geomechanics and Geoengineering, 7(4): 263 282. Hussien, M.N., Tobita, T., Iai, S., Karray, M. 2014. On the influence of vertical loads on the lateral response of pile foundation. Computers and Geotechnics, 55(1):392 403. Hussien, M.N., Tobita, T., Iai, S., and Rollins, K.M. 2010. Soil pile separation effect on the performance of a pile group under static and dynamic lateral load. Canadian Geotechnical Journal, 47(11): 1234 1246. Iai, S., Matsunaga, Y., and Kameoka, T. 1992. Strain Space Plasticity Model for Cyclic Mobility. Soils and Foundations, Japanese Geotechnical Society, 32(2): 1 15. Karthigeyan, S., Ramakrishna, V.V.G.S.T., Rajagopal, K. 2006. Influence of vertical load on the lateral response of piles in sand. Computers and Geotechnics Journal, 33(2): 121 131. Karthigeyan, S., Ramakrishna, V.V.G.S.T., Rajagopal, K. 2007. Numerical investigation of the effect of vertical load on the lateral response of piles. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 133(5): 512 521. Ozutsumi, O., Tamari, Y., Oka, Y., Ichii, K., Iai, S., and Umeki, Y. 2003. Modeling of Soil Pile Interaction Subjected to Soil Liquefaction in Plane Strain Analysis. In Proceeding of the 38th Japan National Conference on Geotechnical Engineering, Akita, Japan, pp. 1899 1900. Tobita, T., Iai, S., and Rollins, K. M. 2006. Numerical Analysis of Full Scale Lateral Load Tests of A 3 5 Pile Group. In Proceeding of the 1st European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland. Zhang, L., McVay, M. C., and Lai, P. 1999. Numerical Analysis of Laterally Loaded 3 3 to 7 3 Pile Groups in Sands. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125(11):936 946.