Experimental Assessment of p-y Curves for Piles in Saturated Medium Dense Sand at Shallow Depths

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1 Experimental Assessment of p-y Curves for Piles in Saturated Medium Dense Sand at Shallow Depths Xiaowei Wang 1, S.M.ASCE, Aijun Ye 2 and Jianzhong Li 3 1 PhD Candidate, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai , China. 10_xiaoweiwang@tongji.edu.cn 2 Professor, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai , China. yeaijun@tongji.edu.cn 3 Professor, State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai , China. lijianzh@tongji.edu.cn (Corresponding author) ABSTRACT: The reliability of numerical models for pile behavior under lateral loading using the p-y relationship proposed by the American Petroleum Institute (API) has been questioned by many researchers. This study presents the development of experimental p-y relationships for piles at shallow depths (less than 1.0 m) in fully saturated medium dense sand. A steel pile was embedded into the sand and fixed at the bottom of a laminar container. Lateral loadings were applied on the pile head for the quasi-static testing using displacement-control technique. The commonly used p-y derivation method was then adopted to develop the experimental p-y curves. Subsequently, distributions of bending moment, shear force, soil reaction, rotation and lateral displacement were presented. Test results exhibit p-y curves that are more flexible (lower initial stiffness) and stronger (greater ultimate strength) at the shallow depths than those proposed by the API. The lateral load-displacement relationship obtained using numerical simulations based on the developed experimental p-y curves are found to match well with the measured responses; therefore, it is concluded that the developed experimental p-y relationships reasonably predict the lateral behavior of piles. Key words: Pile; Quasi-static test; Lateral behavior; Experimental p-y method; Saturated sand.

2 INTRODUCTION The accurate and efficient prediction on the behavior of pile foundations under lateral loading is a critical issue that widely affects the evaluation of the performance of bridge structures. In this regard, several numerical modelling approaches have been proposed for reliable design of pile foundations. Among them, the p-y soil springs (p is the soil-pile reaction and y is the pile deflection) for representation of lateral soil resistance in the Beam-on-Winkler-Foundation model are popular among academic researchers and practicing engineers (Matlock et al. 1978; Boulanger et al. 1999; Limkatanyu et al. 2009; Wang et al. 2016). This appeal is due to the fact that the p-y method has the advantage of accurately predicting pile displacements compared with more simplified limit equilibrium approaches, such as Dobry et al. (2003) and He et al. (2009), and it also has the merit of computational efficiency when compared to the three-dimensional Finite Element Models (FEMs) (e.g. Finn and Fujita 2002 and Giannakos et al. 2012). Most commonly, the p-y derivation method is adopted to produce the experimental p-y curves; that is pile curvatures are obtained through glued strain gauges along piles, and then translated into deflection by double integration, and into soil reaction by double derivation. Since the mid-1960s, extensive experimental studies have been conducted to develop various p-y models to represent pile behavior in cohesionless soil (Kondner 1963; Reese et al. 1974; O Neill and Murchison 1983; Yan and Byrne 1992; Tak Kim et al. 2004; Choo and Kim 2015). Among them, the p-y relationship proposed by O Neill and Murchison (1983) was most widely used because it is adopted as foundation design standard by the American Petroleum Institute (API 2011), hereafter called API p-y relationship for convenience. However, the reliability of results provided by this approach has been questioned by many researchers (e.g. Dyson and Randolph 2001, Achmus et al and Haiderali et al. 2013). One of the issues is the overestimation of initial stiffness and underestimation of ultimate strength for p-y curves of very dense sand (Yan and Byrne 1992; Zhu et al. 2015). As to the p-y relationship at shallow depths in fully saturated medium dense sand that may render greater lateral displacement for a given pile foundation, the validity of API p-y relationships have rarely been examined to the authors knowledge. This study aims to investigate the validity of the widely used API p-y relationship for piles at shallow depths in fully saturated medium dense sands. To this end, a quasi-static test was carried out on an instrumented steel pipe subjected to lateral loading. The p-y derivation method was used to develop the experimental p-y curves. Differences between the derived p-y curves and API p-y relationship were then compared. Next, based on either the experimental or the API p-y relationships, the quasi-static test was simulated using the Beam-on-Nonlinear-Winkler-Foundation

3 (BNWF) model in the open source platform, OpenSees (McKenna 2011). Finally, the derived global force-displacement relationship from the recorded data and the numerical simulations were compared. TEST SETUP As seen in Fig.1, the experimental setup consists of a steel pile embedded into a laminar container full of homogeneous saturated medium dense sand, and subject to lateral loading supplied by a servo-controlled actuator. The inside dimension of the laminar container are 2.0 m (length) 1.5 m (width) 2.0 m (height). The instrumented steel pipe was bolted to the bottom of the soil container before placement of the saturated sand layers. The homogeneous saturated sand layers were placed using wet pluviation. Details on the pile and soil properties are described as follows. Actuator LVDT Steel pipe Ribbed stiffener Reaction wall Laminar container (a) (b) Fig.1 Steel pipe in saturated medium dense sand: (a) physical photograph of test model and (b) schematic diagram. Pile Properties The steel pile was constructed in manufactory using a Q345 (nominal yielding stress of 345 MPa) steel pipe with an outside diameter of 12.1 cm and nominal wall thickness of 0.8 cm. The total length of the steel pile is 2.8 m with an embedded depth of 1.9 m and aboveground height of 0.9 m. Four triangular ribbed stiffeners with width of 15 cm and thickness of 0.5 cm were welded to strengthen the welded connection between the pile head and the highly rigid triangular steel cap. Soil Properties and Placement The Shanghai sand was used for the saturated soil layers. As seen in Fig.2, the Page 3

4 sand is poorly graded with a mean grain size of 0.33 mm, a coefficient of uniformity of 2.06, maximum and minimum dry densities of and g/cm 3, respectively. To achieve a fully saturated medium dense sand layers with relative density around 50%, 20 cm height of pure water was pumped into the container before the soil placement. The air pluviation approach was adopted to place the sand into the container, which is described as below. A large steel bucket full of weighted dry sand was suspended over a long hopper and the dry sand was dropped into the water slowly and evenly through the hopper that is just beyond the water surface. After the sand was compacted to reach a scheduled height, another 10 cm height of water was pumped into the container very slowly. The placement of the next soil layer continued with this procedure. Note that, during the soil placement, the water level kept 5 to 10 cm higher than the soil surface to achieve a fully saturated circumstance. Finally, a total dropped mass of 8730 kg and volume of 5.7 m 2 of the sand were placed into the laminar container, which corresponds to an average relative density of 49%. The placed soil and steel pile were left standing overnight to ensure a stable saturated ground. Before the lateral loading, three samples of the sand were taken randomly from the laminar container and a mean saturated density of g/cm 3 was obtained. Fig.2 Particle size distribution of the Shanghai sand Instrumentation and Test Procedure As can been in Fig. 1(b), the steel pile were heavily instrumented with strain gauges and Linear Variable Differential Transformers (LVDTs) to monitor the curvatures and deflections of the steel pile during the lateral loading. Specifically, 21 pairs of strain gauges were glued on the outer surface of the steel pile with an interval of 10 cm. Two LVDTs were assigned at the positions of pile head and aboveground height of 0.5 m, respectively. The motivation of installing these two LVDTs is to obtain the boundary conditions for the development of experimental p-y curves in the p-y derivation method, which will be expatiated hereinafter. Page 4

5 A lateral displacement of 10 cm is applied on the steel cap. The behavior of the steel remained in elastic state during the loading procedure, which helps to reduce the uncertainties of the production of elasticity modulus E and sectional inertia moment I of the steel pile, and enhance the reliability of the p-y derivation method. RESULTS AND INTERPRETATION Global Load-Displacement Relationship The recorded load-displacement relationship is shown in Fig.3. The fluctuation of the lateral force around the displacement of m might be due to the soil mechanical properties changed from elasticity to plasticity. Note that the steel pile remained elastic in the test. Fig.3 Global load-displacement relationship Development of Experimental p-y Curves Methodology The most commonly used p-y derivation method was adopted in this study. Specifically, the bending moment distributions along the steel pile were obtained from the strain gauges. The bending moment distribution was then expressed mathematically to obtain (a) the soil reaction through double derivative and (b) the pile deflection by double integration, as expressed in Eq. (1) and (2). 2 dm p = (1) 2 dz M y = ( ϕdz) dz = dz dz EI (2) where p is the soil reaction per unit length of the pile; M is the bending moment at depth of z; y is the lateral deflection of the pile; φ is the sectional curvature, obtained from the ratio of the difference between the compression and tension Page 5

6 strains measured at a given depth to the lateral distance between these two strain gauges; EI is the sectional stiffness of the pile. The recorded bending moment could be expressed mathematically using many fitting technologies, including high-order polynomial function, piecewise polynomial function, polynomial-trigonometry combined function, and weighted residuals (e.g. Kong and Zhang 2006; Yang and Liang 2006; Brandenberg et al. 2010; Sinnreich and Ayithi 2014). It is worth to note that, in theoretical, the aboveground bending moment increases linearly with the pile height, whereas the underground bending moment develops nonlinearly with the depth due to the nonlinear behavior of the sand under lateral loading. In this regard, the piecewise polynomial fitting technology was used in this study; that is the aboveground bending moment was fitted with linear polynomial, as expressed in Eq. (3), while the underground bending moment was mathematically expressed as fractional fifth-order polynomial function in Eq. (4), which was introduced by Wilson (1998). b M = a + a z (3) a 0 1 M = b + bz+ b z + b z + b z + b z (4) where ai ( i= 0,1) and bj ( j= 0,1,2,3,4,5) are constant coefficients. The motivation for the exponent of 2.5 (rather than 2) is to meet the requirement of zero soil reaction ( p = 0) at the soil surface ( z = 0) ; that is the second derivation of Eq. (4) equals to zero at z = 0, as expressed as Eq. (5). pz ( ) = 3.75bz 6bz 12bz 20bz (5) The coefficients of Eq. (3) were first obtained through the first-order polynomial fitting command in Matlab (MathWorks 2015). It is worth to note that the coefficient a 1 in Eq. (3) corresponds to the shear force of the aboveground pile, which should be equal to the lateral load provided by the actuator. In this regard, the sectional stiffness was calibrated to be 675 kn m 2 through the target function of minimum error between the fitted coefficient a 1 and the actuator load. Then the Eq. (3) was double integrated to produce the aboveground pile deflection. Two additional coefficients generated from the integration procedure were determined using the boundary conditions of recorded pile deflections at two LVDTs. The pile deflection and rotation at the soil surface was then computed to be the boundary conditions for the underground pile. Also, continuous requirements of the pile bending moment and shear force at z = 0 should be satisfied by using the equations of b0 = a0 and b1 = a1. The remaining coefficients in Eq. (4) were determined through the multivariable best-fit command for user-defined functions in Matlab (MathWorks 2015). After that, underground soil reactions and pile deflections were derived through Eq. (5) and double integration of Eq. (4), respectively. Page 6

7 Derived p-y Curves Fig.4 presents an example of derivation procedure for the experimental p-y curves. Distributions of bending moment, shear force, soil reaction, rotation and displacement along the pile at the maximum loading moment are illustrated. Specifically, the gray circles in Fig.4 represented the recorded bending moment along the pile at the maximum load (displacement of 0.1 m). The bending moment profile increased with increasing depth up to approximately 1.0 m and then showed decreasing tendency. The piecewise first-order and fractional fifth-order polynomial functions fitted the measured bending moment reasonably well. Also, it is worth to note that a negative bending moment was observed at pile head because of the enhanced pile-cap connection by ribbed stiffeners. Fig.4 p-y curve derivation procedure for rigid pile By gathering the pile deflections and soil reactions at all loading steps, the experimental p-y curves for different depths were developed. Fig.5 illustrates the p-y curves from depth of 0.1 to 0.9 m. For better inspection, the raw test data was smoothed using the locally weighted scatter plot smooth technology in Matlab (MathWorks 2015). Note that the p-y curves at deeper depths were not presented because the pile deflections were quite small and the raw test data seemed tousled without clear developments. As can been in Fig.5, most of the experimental p-y curves exhibited greater ultimate soil reaction compared with the API p-y relationships. The experimental soil reaction lower than the API at the depth of 0.9 m might be due to the insufficient pile deflection required to trigger the ultimate soil reaction. Also, ultimate soil reactions were not obviously observed at depths of 0.7 and 0.8 m. In general, the experimental p-y curves in this study can been expressed using trilinear regressions. As seen in Fig.5(a), two control points were picked from the curve to best fit the initial stiffness k 1 and hardening stiffness k 2. A flat line is then assumed to develop the simplified trilinear p-y relationship. The mechanical properties of this proposed trilinear p-y relationships and the initial stiffness of the Page 7

8 API p-y relationships were both listed in Table 1. Apparently, the experimental p-y curves displayed generally softer behavior than the API p-y relationships with respect to the initial stiffness of the curves. In addition, both the initial and hardening stiffness of the experimental p-y curves increased with increasing depths. Hence, it is concluded that the p-y curves at shallow depths derived from this experimental study exhibit softer (lower initial stiffness) and stronger (greater ultimate strength) properties than those recommended by the API (2011). Fig.5 Derived p-y relationships Table.1 Mechanical properties of experiment-derived p-y curves Depth p 1 y 1 p 2 y 2 k 1 k 2 API initial stiffness m kn/m m kn/m m kn/m/m kn/m/m kn/m Page 8

9 Verification of Experimental p-y Curves BNWF Model The validity of the developed p-y curves in this study was verified through FEM in OpenSees. The FEM used a BNWF model, where elastic beam-column elements are used to present the steel pile and closely spaced (0.1 m) nonlinear soil springs were used to represent the soil resistance. Fig.6 shows the FEM schematic in which the nodes for the elastic beam-column elements were spaced at 0.1 m. The pile head and the lateral loading nodes were connected with a rigid link to represent the highly rigid property of the cap. It is worth to note that the ribbed stiffeners welded at the pile-cap connection prevented the free rotation property at pile head. To achieve an accurate simulation result, a rotational spring was added to the loading node with the moment-rotation constitutive model derived from the above introduced p-y derivation method; that is the moment-rotation relationship at pile head. As can be seen in Fig. 7, an elastic perfectly-plastic model was proposed based on the law of energy conservation. For depths from 0.1 to 0.9 m, either the proposed trilinear p-y curves in this study (Fig.5 and Table 1) or the API p-y relationships were adopted in the FEM, whereas for the depths below 0.9 m, the API p-y relationships were utilized for convenience. A lateral control displacement of 0.1 m was assigned at the loading node of the FEM to simulate the quasi-static testing. Fig.6 BNWF-based FEM schematic Fig.7 Moment-rotation constitutive diagram of the steel pile model for the rotational spring Experimental and Numerical Comparison Fig.8 presents the numerical results of the FEMs using (a) the conventional API Page 9

10 p-y relationships along the pile and (b) the proposed trilinear p-y relationships at shallow depths, and their comparisons to the experimental result. As can be seen in Fig.8, the FEM with the proposed trilinear p-y relationships in this study predicted the test result accurately, both the initial stiffness and the further development of the lateral strength, whereas the FEM using the conventional API p-y relationships underestimated the strength of the pile, which may be a risky and undesirable numerical approach for the seismic design of pile foundations in saturated medium dense sand. The accurate coincidence between the numerical result of this study and the experimental data validated the derivation methodology used for the development of experimental p-y curves. Fig.8 Comparison of global lateral force and displacement relationship CONCLUSION Quasi-static lateral loading test was carried out in this study to investigate the validity of conventional API p-y relationships at shallow depths for pile foundations embedded in fully saturated medium dense sand. It is concluded that the conventional API p-y relationships may underestimate the lateral strength of piles embedded in fully saturated medium dense sand. The trilinear p-y relationships proposed based on the experimental p-y curves were capable to predict the global force and displacement response of the pile foundation accurately. Future studies are planned to establish the p-y constitutive models at shallow depths for piles in saturated sand with different relative densities. ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China Page 10

11 (Grant No ) and the Ministry of Science and Technology of China (Grant No. SLDRCE 15-B-05). All staffs in the Multi-Functional Shaking Table Laboratory of Tongji University at Jiading Campus are greatly acknowledged, especially Drs. Yan Xu and Chengyu Yang who provided lots of insightful suggestions to our experiments. Special thanks to Dr. Abdollah Shafieezadeh, who provided insightful comments to improve this paper. Any opinions, findings, and conclusions expressed are those of the authors, and do not necessarily reflect those of the sponsoring organizations. REFERENCES Achmus, M., Kuo, Y. S., and Abdel-Rahman, K. (2009). Behavior of monopile foundations under cyclic lateral load. Computers and Geotechnics, 36(5), API. (2011). Geotechnical and foundation design considerations. American Petroleum Institute, Washington, D.C. Boulanger, R. W., Curras, C. J., Kutter, B. L., Wilson, D. W., and Abghari, A. (1999). Seismic soil-pile-structure interaction experiments and analyses. Journal of Geotechnical and Geoenvironmental Engineering, 125(9), Brandenberg, S., Wilson, D., and Rashid, M. (2010). Weighted residual numerical differentiation algorithm applied to experimental bending moment data. Journal of Geotechnical and Geoenvironmental Engineering, American Society of Civil Engineers, 136(6), Choo, Y. W., and Kim, D. (2015). Experimental development of the p-y relationship for large-diameter offshore monopiles in sands: centrifuge tests. Journal of Geotechnical and Geoenvironmental Engineering, (2010), Dobry, R., Abdoun, T., O Rourke, T. D., and Goh, S. H. (2003). Single piles in lateral spreads : field bending moment evaluation. Journal of Geotechnical and Geoenvironmental Engineering, 129(10), Dyson, G. J., and Randolph, M. F. (2001). Monotonic lateral loading of piles in calcareous sand. Journal of Geotechnical and Geoenvironmental Engineering, 127(4), Finn, W. D.. D. L., and Fujita, N. (2002). Piles in liquefiable soils: seismic analysis and design issues. Soil Dynamics and Earthquake Engineering, 22(9-12), Giannakos, S., Gerolymos, N., and Gazetas, G. (2012). Cyclic lateral response of piles in dry sand: Finite element modeling and validation. Computers and Geotechnics, Elsevier Ltd, 44, Haiderali, A., Cilingir, U., and Madabhushi, G. (2013). Lateral and axial capacity of monopiles for offshore wind turbines. Indian Geotechnical Journal, 43(3), Page 11

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