Note on the Interaction Factor for Two Laterally Loaded Piles

This technical note revisits the interaction factors for two piles under lateral loading by means of a rigorous analytical method. The basic idea of the approach presented is to decompose the problem into an extended elastic soil and two fictitious piles having Young’s modulus equal to the difference between the modulus of the real pile and the surrounding soil. By considering the displacement compatibility condition, the pile–soil interaction problem is found to be governed by a Fredholm equation of the second kind. The displacement and bending moment distribution along the fictitious piles, and consequently, the desired interaction factor at the pile head are obtained. Comparison with existing solutions validates the accuracy of the present formulation and confirms that the conventional interaction factor approach would exaggerate the interaction effect for long flexible piles. Some numerical examples are presented to illustrate the influences of the pile spacing, pile–soil stiffness ratio, pile slenderness ratio, and departure angle of the loading direction on the calculated results. A set of interaction factor charts is also provided.     

Simplified Lateral Load Analyses of Fixed-Head Piles and Pile Groups

The characteristic load method (CLM) can be used to estimate lateral deflections and maximum bending moments in single fixed-head piles under lateral load. However, this approach is limited to cases where the lateral load on the pile top is applied at the ground surface. When the pile top is embedded, as in most piles that are capped, the additional embedment results in an increased lateral resistance. A simple approach to account for embedment effects in the CLM is presented for single fixed-head piles. In practice, fixed-head piles are more typically used in groups where the response of an individual pile can be influenced through the adjacent soil by the response of other nearby piles. This pile–soil–pile interaction results in larger deflections and moments in pile groups for the same load per pile compared to single piles. A simplified procedure to estimate group deflections and moments was also developed based on the p-multiplier approach. Group amplification factors are introduced to amplify the single pile deflection and bending moment to reflect pile–soil–pile interaction. The resulting approach lends itself well to simple spreadsheet computations and provides good agreement with other generally accepted analytical tools and with values measured in published lateral load tests on groups of fixed-head piles.     

Pile Spacing Effects on Lateral Pile Group Behavior: Analysis

Using the results from three full-scale lateral pile group load tests in stiff clay with spacing ranging from 3.3 to 5.65, computer analyses were performed to back-calculate p multipliers. The p multipliers, which account for reduced resistance due to pile–soil–pile interaction, increased as pile spacing increased from 3.3 to 5.65 diameters. Extrapolation of the test results suggests that group reduction effects can be neglected for spacings greater than about 6.5 for leading row piles and 7–8 diameters for trailing row piles. Based on analysis of the full-scale test results, pile behavior can be grouped into three general categories, namely: (1) first or front row piles; (2) second row piles; and (3) third and higher row piles. p multiplier versus normalized pile spacing curves were developed for each category. The proposed curves yield p multipliers which are higher than those previously recommended by AASHTO in 2000, the US Army in 1993, and the US Navy in 1982 based on limited test data, but lower values than those proposed by Reese et al. in 1996 and Reese and Van Impe in 2001. The response (load versus deflection, maximum moment versus load, and bending moment versus depth) for each row of the pile groups computed using GROUP and Florida Pier generally correlated very well with measurements from the full-scale tests when the p multipliers developed from this test program were employed.     

Strain Wedge Model Capability of Analyzing Behavior of Laterally Loaded Isolated Piles, Drilled Shafts, and Pile Groups

This paper demonstrates the application of the strain wedge (SW) model to assess the response of laterally loaded isolated long piles, drilled shafts, and pile groups in layered soil (sand and/or clay) and rock deposits. The basic goal of this paper is to illustrate the capabilities of the SW model versus other procedures and approaches. The SW model has been validated and verified through several comparison studies with model- and full-scale lateral load tests. Several factors and features related to the problem of a laterally loaded isolated pile and pile group are covered by the SW model. For example, the nonlinear behavior of both soil and pile material, the soil-pile interaction (i.e., the assessment of the p-y curves rather than the adoption of empirical ones), the potential of soil to liquefy, the interference among neighboring piles in a pile group, and the pile cap contribution are considered in SW model analysis. The SW model analyzes the response of laterally loaded piles based on pile properties (pile stiffness, cross-sectional shape, pile-head conditions, etc.) as well as soil properties. The SW model has the capability of assessing the response of a laterally loaded pile group in layered soil based on more realistic assumptions of pile interference as compared to techniques and procedures currently employed or proposed.     

Simplified Approach for the Seismic Response of a Pile Foundation

Pseudostatic approaches for the seismic analysis of pile foundations are attractive for practicing engineers because they are simple when compared to difficult and more complex dynamic analyses. To evaluate the internal response of piles subjected to earthquake loading, a simplified approach based on the “p-y” subgrade reaction method has been developed. The method involves two main steps: first, a site response analysis is carried out to obtain the free-field ground displacements along the pile. Next, a static load analysis is carried out for the pile, subjected to the computed free-field ground displacements and the static loading at the pile head. A pseudostatic push over analysis is adopted to simulate the behavior of piles subjected to both lateral soil movements and static loadings at the pile head. The single pile or the pile group interact with the surrounding soil by means of hyperbolic p-y curves. The solution derived first for the single pile, was extended to the case of a pile group by empirical multipliers, which account for reduced resistance and stiffness due to pile-soil-pile interaction. Numerical results obtained by the proposed simplified approach were compared with experimental and numerical results reported in literature. It has been shown that this procedure can be used successfully for determining the response of a pile foundation to “inertial” loading caused by the lateral forces imposed on the superstructure and “kinematic” loading caused by the ground movements developed during an earthquake.     

Pile Spacing Effects on Lateral Pile Group Behavior: Load Tests

To investigate group interaction effects as a function of pile spacing, full-scale cyclic lateral load tests were performed on pile groups in stiff clay spaced at 3.3, 4.4, and 5.65 pile diameters in the direction of loading with as many as five rows of piles. Group interaction effects decreased considerably as pile spacing increased from 3.3 to 5.65D. Lateral resistance was a function of row location in the group, rather than location within a row. For a given deflection, the leading (first) row piles carried the greatest load, while the second and third row piles carried successively smaller loads. Fourth and fifth row piles carried about the same load as the third row piles. For a given load, the maximum bending moments in the trailing row piles were greater than those in the lead row, but these effects decreased as spacing increased. Cyclic loading reduced the peak load by about 15% after 15 cycles; however, distribution of load within the pile group was essentially the same as at the peak load. Gaps significantly reduced resistance for small deflections.     

Cyclic Lateral Load Behavior of a Pile Cap and Backfill

A series of static cyclic lateral load tests were performed on a full-scale 4×3 pile group driven into a cohesive soil profile. Twelve 324-mm steel pipe piles were attached to a concrete pile cap 5.18×3.05?m in plan and 1.12?m in height. Pile–soil–pile interaction and passive earth pressure provided lateral resistance. Seven lateral load tests were conducted in total; four tests with backfill compacted in front of the pile cap; two tests without backfill; and one test with a narrow trench between the pile cap and backfill soil. The formation of gaps around the piles at larger deflections reduced the pile–soil–pile interaction resulting in a degraded linear load versus deflection response that was very similar for the two tests without backfill and the trenched test. A typical nonlinear backbone curve was observed for the backfill tests. However, for deflections greater than 5 mm, the load-deflection behavior significantly changed from a concave down shape for the first cycle to a concave up shape for the second and subsequent cycles. The concave up shape continued to degrade with additional cycles past the second and typically became relatively constant after five to seven cycles. A gap formed between the backfill soil and the pile cap, which contributed to the load-deflection degradation. Crack patterns and sliding surfaces were consistent with that predicted by the log spiral theory. The results from this study indicate that passive resistance contributes considerably to the lateral resistance. However, with cyclic loading the passive force degrades significantly for deflections greater than 0.5% of the pile cap height.     

Nonlinear Efficiency of Bored Pile Group under Lateral Loading

A 3×3 bored pile group consisting of nine cast-in-drilled-hole reinforced concrete shafts and a comparable single-shaft were subjected to reversed cyclic, lateral head loading to investigate group interaction effects across a wide range of lateral displacements. The piles had the same diameter of d = 0.61?m and similar soil conditions; however, various equipment constraints led to two differences: (1) a fixed head (zero rotation) boundary condition for the single pile versus minor pile cap rotation in the vertical plane for the group and (2) shaft longitudinal reinforcement ratios of 1.8% for the single pile and 1% for the group piles. To enable comparisons between the test results, a calibrated model of the single pile (1.8% reinforcement) was developed and used to simulate the response of a single shaft with 1% reinforcement. Additional simulations of the pile group were performed to evaluate the effects of cap rotation on group response. By comparing the simulated responses for common conditions, i.e., 1% reinforcing ratio and zero head rotation, group efficiencies were found to range from unity at lateral displacements <0.004×d to 0.8 at small displacements ～ 0.01–0.02×d and up to 0.9 at failure (displacements >0.04×d). Hence, we find that group efficiency depends on the level of nonlinearity in the foundation system. The general group efficiency, although not its displacement-dependence, is captured by p-multipliers in the literature for reinforced concrete, fixed-head piles.     

Ultimate Lateral Resistance of Pile Groups in Sand

Experimental investigations on model pile groups of configuration 1 × 1, 2 × 1, 3 × 1, 2 × 2, and 3 × 2 for embedment length-to-diameter ratios L∕d = 12 and 38, spacing from 3 to 6 pile diameter, and pile friction angles δ = 20° and 31°, subjected to lateral loads, were conducted in dry Ennore sand obtained from Chennai, India. The load-displacement response, ultimate resistance, and group efficiency with spacing and number of piles in a group have been qualitatively and quantitatively investigated. Analytical methods have been proposed to predict the ultimate lateral capacity of single pile and pile groups. The proposed methods account for pile friction angle, embedment length-to-diameter ratio, the spacing of piles in a group, pile group configuration, and soil properties. These methods are capable of predicting the lateral capacity of piles and pile groups reasonably well as noted and substantiated by the comparison with the experimental results of the writers and other researchers.     

Soil–Pile Response to Blast-Induced Lateral Spreading. I: Field Test

Two full-scale experiments using controlled blasting were conducted in the Port of Tokachi on Hokkaido Island, Japan, to assess the behavior of a single pile, a four-pile group, and a nine-pile group subjected to lateral spreading. The test piles were extensively instrumented with strain gauges to measure the distribution of bending moment during lateral spreading which allowed the backcalculation of the loading conditions, as well as the assessment of damage and performance of the piles. Based on the test results, it was concluded that using controlled blasting successfully liquefied the soil, and subsequently induced lateral spreading in the 4–6% surface slope test beds. The free-field soil displacements in the vicinity of the test piles were over 40 cm for both tests. When compared with the results from the single pile case, the effect of pile head restraint from the pile cap improved overall pile performance by decreasing the displacement of the pile groups and lowering the maximum moments in individual piles within each group. Finally, backcalculated soil reactions indicated that the liquefied soil layer imparted insignificant force to the piles. In the companion to this paper (Part II), an assessment of the potential of using the p–y analysis method for single piles and pile groups subjected to lateral spreading is presented.     

Group Interaction Effects on Laterally Loaded Piles in Clay

This paper presents the results of static lateral load tests carried out on 1×2, 2×2, 1×4, and 3×3 model pile groups embedded in soft clay. Tests were carried out on piles with length to diameter ratios of 15, 30, and 40 and three to nine pile diameter spacing. The effects of pile spacing, number of piles, embedment length, and configuration on pile-group interaction were investigated. Group efficiency, critical spacing, and p multipliers were evaluated from the experimental study. The experimental results have been compared with those obtained from the program GROUP. It has been found that the lateral capacity of piles in 3×3 group at three diameter spacing is about 40% less than that of the single pile. Group interaction causes 20% increase in the maximum bending moment in piles of the groups with three diameter spacing in comparison to the single pile. Results indicate substantial difference in p multipliers of the corresponding rows of the linear and square pile groups. The predicted field group behavior is in good agreement with the actual field test results reported in the literature.     

Soil-Pile Response to Blast-Induced Lateral Spreading. II: Analysis and Assessment of the p–y Method

This paper presents an assessment of the potential of using the p–y analysis method for single piles and pile groups subjected to lateral spreading. The computed responses were compared with the results from the full-scale lateral spreading tests in Japan as presented in the Part I companion paper. The responses of the single piles subjected to lateral spreading were determined by imposing the known free-field soil movement profile to the Winkler spring model. The soil springs of nonliquefied soils used in this study were based upon standard p–y springs whereas zero spring stiffness was used for liquefied soils. For the case of pile groups, they were modeled as an equivalent single pile with a rotational spring at the pile head to simulate effect of pile head restraint. A decrease of soil spring stiffnesses using the p-multiplier approach was used to account for pile group effects. Based on the results of analyses, the computed responses of all sets of the test piles using a single set of baseline soil properties were in good agreement with the measured responses. These results suggest that the p–y analysis method may be used to estimate the behavior of piles subjected to lateral spreading.     

Response of Laterally Loaded Large-Diameter Bored Pile Groups

This paper presents results of full-scale lateral load tests of one single pile and three pile groups in Hong Kong. The test piles, which are embedded in superficial deposits and decomposed rocks, are 1.5 m in diameter and approximately 30 m long. The large-diameter bored pile groups consist of one two-pile group at 6 D (D = pile diameter) spacing and one two-pile and one three-pile group at 3 D spacing. This paper aims to investigate the nonlinear response of laterally loaded large-diameter bored pile groups and to study design parameters for large-diameter bored piles associated with the p-y method using a 3 D finite-element program, FLPIER. Predictions using soil parameters based on published correlations and back-analysis of the single-pile load test are compared. It is found that a simple hyperbolic representation of load-deflection curves provides an objective means to determine ultimate lateral load capacity, which is comparable with the calculated values based on Broms' theory. Lateral deflections of bored pile groups predicted using the values of the constant of horizontal subgrade reaction, suggested by Elson and obtained from back-analysis of the single pile load test, are generally in good agreement with the measurements, especially at low loads.     

Development of Downdrag on Piles and Pile Groups in Consolidating Soil

Development of pile settlement (downdrag) of piles constructed in consolidating soil may lead to serious pile foundation design problems. The investigation of downdrag has attracted far less attention than the study of dragload over the years. In this paper, several series of two-dimensional axisymmetric and three-dimensional numerical parametric analyses were conducted to study the behavior of single piles and piles in 3×3 and 5×5 pile groups in consolidating soil. Both elastic no-slip and elasto-plastic slip at the pile–soil interface were considered. For a single pile, the downdrag computed from the no-slip elastic analysis and from the analytical elastic solution was about 8–14 times larger than that computed from the elasto-plastic slip analysis. The softer the consolidating clay, the greater the difference between the no-slip elastic and the elasto-plastic slip analyses. For the 5×5 pile group at 2.5 diameter spacing, the maximum downdrag of the center, inner, and corner piles was, respectively, 63, 68, and 79% of the maximum downdrag of the single pile. The reduction of downdrag inside the pile group is attributed to the shielding effects on the inner piles by the outer piles. The relative reduction in downdrag (Wr) in the 5×5 pile group increases with an increase in the relative bearing stiffness ratio (Eb/Ec), depending on the pile location in the group. Compared with the relative reduction in dragload (Pr), Wr at the corner pile is less affected by the group interaction for a given surcharge load. This suggests that the use of sacrificing piles outside the pile group will be more effective on Pr than on Wr. Based on the three cases studied, the larger the number of piles in a group, the greater the shielding effects on Wr. Relatively speaking, Wr is more sensitive to the total number of piles than to the pile spacing within a pile group.     

Slope Stabilizing Piles and Pile-Groups: Parametric Study and Design Insights

This paper uses a hybrid method for analysis and design of slope stabilizing piles that was developed in a preceding paper by the writers. The aim of this paper is to derive insights about the factors influencing the response of piles and pile-groups. Axis-to-axis pile spacing (S), thickness of stable soil mass (Hu), depth (Le) of pile embedment, pile diameter (D), and pile group configuration are the parameters addressed in the study. It is shown that S = 4D is the most cost-effective pile spacing, because it is the largest spacing that can still generate soil arching between the piles. Soil inhomogeneity (in terms of shear stiffness) was found to be unimportant, because the response is primarily affected by the strength of the unstable soil layer. For relatively small pile embedments, pile response is dominated by rigid-body rotation without substantial flexural distortion: the short pile mode of failure. In these cases, the structural capacity of the pile cannot be exploited, and the design will not be economical. The critical embedment depth to achieve fixity conditions at the base of the pile is found to range from 0.7Hu to 1.5Hu, depending on the relative strength of the unstable ground compared to that of the stable ground (i.e., the soil below the sliding plane). An example of dimensionless design charts is presented for piles embedded in rock. Results are presented for two characteristic slenderness ratios and several pile spacings. Single piles are concluded to be generally inadequate for stabilizing deep landslides, although capped pile-groups invoking framing action may offer an efficient solution.     

Dynamic Soil–Structure Interaction of Bridge Substructure Subject to Vessel Impact

The paper describes the in situ investigation, site stratigraphy, field monitoring, data reduction, and subsequent time-domain analysis of soil–structure interaction from a full scale vessel impact loading of a bridge pier at the St. George Island Causeway. The in situ investigation included standard penetration testing, electric cone, dilatometer, and pressuremeter testing to identify soil stratigraphy, engineering properties (strength and moduli), and axial and lateral static pile resistance (T–z, and P–y). Field instrumentation included soil total stress and pore pressure gauges in front of and behind the pile cap, a fully instrumented pile (strain gauges along length), dynamic load cells to monitor barge impact loads, and accelerometers to monitor pier accelerations, velocities, and displacements. Analyses of the field data reveal significant dynamic forces within the soil–structure system as a result of the duration and magnitude of the loading. Inertia from the piers, cap, and piles provide significant resistance in the early portion of the impact. However, postpeak inertia (i.e., pier deceleration) resulted in maximum deformations of the pier. Soil damping provided most of the resisting force at the peak barge loading, whereas static soil resistance dominated at the peak lateral displacement. Time-domain finite element analysis of an impact event employing viscous soil dashpots, nonlinear P–y and T–z springs with nonlinear beam, and shell elements for the pier, cap, and piles resulted in reasonable load displacement predictions.     

Failure Mechanisms of Pile Foundations in Liquefiable Soil: Parametric Study

This paper presents the response of piles in liquefiable soil under seismic loads. The effects of soil, pile, and earthquake parameters on the two potential pile failure mechanisms, bending and buckling, are examined. The analysis is conducted using a two-dimensional plain strain finite difference program considering a nonlinear constitutive model for soil liquefaction, strength reduction, and pile-soil interaction. The depths of liquefaction, maximum lateral displacement, and maximum pile bending moment are obtained for concrete and steel piles for different soil relative densities, pile diameters, earthquake predominant frequencies, and peak accelerations. The potential failure mechanisms of piles identified from the parametric analysis are discussed.     

Centrifuge Modeling of Torsionally Loaded Pile Groups

This paper reports a series of centrifuge model tests on torsionally loaded 1×2, 2×2, and 3×3 pile groups in sand. The objectives of the paper are to investigate: (1) the response of the pile groups subjected to torsion; (2) the way in which the applied torque is transferred in the pile groups; (3) the internal forces mobilized in these torsionally loaded pile groups and their contributions to resist the applied torque; and (4) the influence factors that affect the load transfer, such as soil density and pile-cap connection. In these model tests, the group torsional resistances of the pile groups increased monotonically in the test range of twist angles up to 8°. Both torsional and lateral resistances of the individual piles were simultaneously mobilized to resist the applied torque. The torsional resistances were substantially mobilized at small twist angles, while the lateral resistances kept increasing in the whole range of twist angles. Thus, the contribution of the torsional resistances to the applied torque decreased at large twist angles. The piles at different locations in a pile group could develop not only different horizontal displacements, but also different pile–soil–pile interactions and load–deformation coupling effect, hence, the torsional and lateral resistances of the piles are a function of pile location. The soil density had a more significant effect on the torsional resistances than on the lateral resistances of the group piles.     

Seismic Behavior of Batter Piles: Elastic Response

Several aspects of the seismic response of groups containing nonvertical piles are studied, including the lateral pile-head stiffnesses, the “kinematic” pile deformation, and the “inertial” soil-pile-structure response. A key goal is to explore the conditions under which the presence of batter piles is beneficial, indifferent, or detrimental. Parametric analyses are carried out using three-dimensional finite-element modeling, assuming elastic behavior of soil, piles, and superstructure. The model is first used to obtain the lateral stiffnesses of single batter piles and to show that its results converge to the available solutions from the literature. Then, real accelerograms covering a broad range of frequency characteristics are employed as base excitation of simple fixed-head two-pile group configurations, embedded in homogeneous, inhomogeneous, and layered soil profiles, while supporting very tall or very short structures. Five pile inclinations are considered while the corresponding vertical-pile group results serve as reference. It is found that in purely kinematic seismic loading, batter piles tend to confirm their negative reputation, as had also been found recently for a group subjected to static horizontal ground deformation. However, the total (kinematic plus inertial) response of structural systems founded on groups of batter piles offers many reasons for optimism. Batter piles may indeed be beneficial (or detrimental) depending on, among other parameters, the relative size of the overturning moment versus the shear force transmitted onto them from the superstructure.     

Simple Energy-Based Method for Nonlinear Analysis of Incompressible Pile Groups in Clays

This note presents a method for predicting nonlinear response of pile groups in clays, subjected to vertical loads. The method is based on mobilizable strength design (MSD) concepts, in which the mobilized strength is associated with the shear strains developed in the soil. The suggested procedure is incremental, and requires evaluation of a displacement field. A simple procedure of superposition of pattern functions is suggested for the construction of a complete displacement field. The incremental procedure allows for the variation of the displacement field throughout the loading process, according to principles of minimum energy and compatibility requirements among the piles. Essentially, the procedure allows consideration of a nonlinear continuum between the piles. The pattern functions are an adaptive form of the logarithmic function suggested by Randolph and Wroth in 1979. Under small load levels, when the soil is essentially elastic, the procedure yields values comparable to those from the elastic solution of Randolph and Wroth. At larger strain levels, nonlinear pile group response is simulated based on the soil constitutive models specified by the practitioner. The method is applicable to cases where shaft loading does not induce volume changes in the soil. The method is compared with three dimensional finite difference simulation of undrained loading of pile groups with a nonlinear soil constitutive model. Fair agreement is observed.