Theoretical Elastic-Plastic Solution for Laterally Loaded Piles

In this paper, the theoretical solutions of maximum deflection and moment for laterally loaded long piles in a uniform subgrade reaction modulus linear-plastic soil are presented. These solutions are in the form of normalized results and enable easy and exact calculation of the deflection or moment for three head loading conditions. Comparisons between the theoretical solution and a numerical solution established previously showed good agreement.     

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.     

Performance of Long-Driven H-Piles in Granitic Saprolite

There has been much advancement using conceptual models and analytical methods to explain various aspects of pile performance. They are mainly based on the findings of model tests and full-scale pile tests in fine-grained and coarse-grained soils, and driven piles on land are normally less than 40?m. Design methods developed from this data bank of pile geometries and soil conditions for long piles should be treated with caution. In this paper, 13 H-piles of 34–60?m and 7,096?kN capacity founded on granitic saprolite are studied. Among them, two piles were restriked at different time intervals. All piles were axially load tested statically using a maintained load method. In contrast to the short rigid piles founded on weaker soil, their load-transfer mechanism varied with the magnitude of applied load and pile length. They deformed almost linearly at small loads and might have buckled when the loads were large and the creep settlements were found to be length dependent. Existing criteria might not be able to interpret failure loads sometimes, but a pile dynamic analyzer was found to give the best estimate on pile capacity.     

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.     

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.     

Numerical Solution for Laterally Loaded Piles in a Two-Layer Soil Profile

Piles are often embedded in a layered soil profile, such as sand or clay layer underlain by rock. Several existing solutions are available for laterally loaded piles in a layered soil system. However, these solutions are only applicable to constant soil stiffness for each layer. In this paper, a variational approach is employed to numerically solve the problem of laterally loaded piles in layered soils using beam on an elastic foundation model. The soil stiffness can be either constant with depth or linearly varying with depth. The numerical solution is validated against an existing solution for linearly varying soil stiffness in a single soil layer system and an existing solution for a two-layer soil system with constant soil stiffness. Case studies using the proposed solution for field lateral load tests on full size drilled shafts embedded in weak rock with an overlying sand layer are presented. The simplicity and the relative ease of using the solution make it a good alternative approach for estimating the deflection and moment responses of a laterally loaded pile in a two-layer soil profile.     

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.     

Behavior of Piled Raft Foundations Under Lateral and Vertical Loading

This article presents a new method of analysis of piled raft foundations in contact with the soil surface. The soil is divided into multiple horizontal layers depending on the accuracy of solution required and each layer may have different material properties. The raft is modeled as a thin plate and the piles as elastic beams. Finite layer theory is employed to analyze the layered soil while finite element theory is used to analyze the raft and piles. The piled raft can be subjected to both loads and moments in any direction. Comparisons show that the results from the present method agree closely with those from the finite element method. A parametric study for piled raft foundations subjected to either vertical or horizontal loading is also presented.     

Termination Criteria for Jacked Pile Construction and Load Transfer in Weathered Soils

Pile jacking is a piling technique that provides a noise- and vibration-free environment in the construction site. To improve termination criteria for pile jacking and to better understand the behavior of jacked piles, two steel H piles were instrumented, installed at a weathered soil site, and load tested. A set of termination criteria was applied to the test piles, which includes a minimum blow count from the standard penetration test, a specified final jacking force, a minimum of four loading cycles at the final jack force, and a specified maximum rate of pile settlement at the final jacking force. The two test piles passed all required acceptance criteria. Punching shear failure occurred at the failure load for both piles and the shaft resistance consisted of approximately 80% of the pile capacity. Based on the results of field tests in Hong Kong and Guangdong and several centrifuge tests, a relation between the ratio of the pile capacity Pult to the final jacking force PJ and the pile slenderness ratio is established. The Pult/PJ ratio is larger than 1.0 for long piles but may be smaller than 1.0 for short piles. A regression equation is established to determine the final jacking force, which is suggested as a termination criterion for jacked piles. The final jacking force can be smaller than 2.5 times the design load for very long piles, but should be larger than 2.5 times the design load for piles shorter than 37 times the pile diameter.     

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.     

Analysis of Laterally Loaded Piles in Soil with Stiffness Increasing with Depth

This article reports a variational solution and its spreadsheet calculation procedure for the analysis of laterally loaded piles in a soil with stiffness increasing with depth. The aim of the paper is to provide solutions that can be used simply with recourse only to spreadsheet calculation to solve the displacement and bending moment of laterally loaded piles, so that they can be easily applied in practice as an alternative approach to analyze the response of laterally loaded piles.     

Moment/Rotation Effects on Laterally Loaded Drilled Shaft Group Response

Drilled shaft groups are often designed to resist lateral loads for transportation structures. The shaft group capacity usually corresponds to a load being applied at the shaft cap level. However, in abutment wall applications, the lateral load is, in fact, applied well above the cap elevation. Thus, the load is transferred to the cap with an additional moment, causing the cap to deflect and rotate more than if this added moment were absent. As a result, the lateral capacity for a given allowable deflection of the group should be reduced because of this effect. Design engineers usually select or approve the allowable deflection at the top of the abutment wall. However, deflection at the cap level is needed to design the group capacity. The main objective of this paper is to report the results from a series of finite-element analyses on abutment wall cap configurations to study the effect of moment on the capacity of the shaft group under lateral load. A scaling factor is defined as the ratio between the group capacity for load applied at a given height above the cap and the group capacity for load applied at the bottom of the cap, and it was found to be dependent on the wall height, the spacing between shafts, and the cap deflection level, and more or less independent of the soil type, the cap thickness, and the shaft diameter. The ratio between the deflection at the top of the abutment wall and the deflection at the cap was found to be dependent on the wall stiffness (wall thickness to wall height ratio).     

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.     

Experimental Study of Eccentrically Loaded Raft with Connected and Unconnected Short Piles

Piled raft foundations are often used when the supporting soil has adequate bearing capacity but the raft settlements exceed allowable values. In traditional practice, long piles with high load capacity are usually used that may lead to two structural problems: the structural collapse of the pile and large strains mobilized in the raft leading to an uneconomic design. This paper presents an experimental study of the effectiveness of using short piles either connected or unconnected to the raft (instead of long piles) on the behavior of an eccentrically loaded raft. The load configuration was designed to simulate rafts under vertical loads and overturning moment. Several arrangements of piles with different lengths and numbers along with the effect of the relative density of the soil and the load eccentricity were studied. Test results indicate that the inclusion of short piles adjacent to the raft edges not only significantly improves the raft bearing pressures but also leads to a reduction in raft settlements and tilts leading to an economical design of the raft. However, the efficiency of the short piles-raft system is dependent on the load eccentricity ratio and pile arrangement. Also, connecting short piles to the raft gives greater improvement in the raft behavior than unconnected piles. Based on test results, the effects of different parameters are presented and discussed.     

Behavior of Step Tapered Bored Piles in Sand under Static Lateral Loading

The behavior of step tapered bored piles in sand, under static lateral loading, was examined by field tests at one site in Kuwait. A total of 14 bored piles including two instrumented piles were installed for lateral loading. The soil profile consists of medium dense sand with weak cementations and no groundwater was encountered in the boreholes. Laboratory tests were carried out to determine the basic soil characteristics and the strength parameters. Both the ultimate lateral capacity and the deflections at applied loads were examined. The results indicate increased lateral load carrying capacity and decreased deflections at different applied loads for the step tapered piles due to the enlargement or strengthening of the upper section of the piles. The advantages of using this type of pile is emphasized including the cost saving resulting from an economical design.     

Behavior of Pile Groups Subject to Excavation-Induced Soil Movement

Centrifuge model tests have been conducted on free-head and capped-head pile groups consisting of two, four, and six piles located adjacent to an unstrutted deep excavation in sand. It is found that when two free- or capped-head piles are arranged in a row parallel to the retaining wall, the interaction effect between piles is insignificant. When two piles are arranged in a line perpendicular to the wall, the existence of a front pile would reduce the detrimental effect of excavation-induced soiled movement on the rear pile. In addition, the provision of a pile cap for two piles arranged in a line would exert a significant influence on the behavior of the pile group. For free-head four- or six-pile groups, the induced bending moment decreases as the number of piles increases. Moreover, the interior piles of the pile group always experience lower bending moments than those of peripheral piles as the latter have more exposure to the excavation-induced soil movement and are thus more adversely affected. For the capped-head four- or six-pile groups, it can be established that the provision of a pile cap would help to moderate the pile-group deflection against soil movement as the rear piles, that are located farther away from the wall and thus less affected by the soil movement, would drag the front piles back.     

Numerical Investigation of the Effect of Vertical Load on the Lateral Response of Piles

The laboratory and field test data on the response of piles under the combined action of vertical and lateral loads is rather limited. The current practice for design of piles is to consider the vertical and lateral loads independent of each other. This paper presents some results from three-dimensional finite-element analyses that show the significant influence of vertical loads on a pile’s lateral response. The analyses were performed in both homogeneous clayey soils and homogeneous sandy soils. The results have shown that the influence of vertical loads on the lateral response of piles is to significantly increase the capacity in sandy soils and marginally decrease the capacity in clayey soils. In general, it was found that the effect of vertical loads in sandy soils is significant even for long piles, which are as long as 30 times the pile width, while in the case of clayey soils, the effect is not significant for piles beyond a length of 15 times the width of the pile. The design bending moments in the laterally loaded piles were also found to be dependent on the level of vertical load on the piles.     

Kinematic Pile Response to Vertical P-wave Seismic Excitation

An analytical solution based on a rod-on-dynamic-Winkler-foundation model is developed for the response of piles in a soil layer subjected to vertical seismic excitation consisting of harmonic compressional waves. Closed-form solutions are derived for: (1) the motion of the pile head; (2) the peak normal strain in the pile, and (3) the group effect between neighboring piles. The solutions are expressed in terms of a dimensionless kinematic response factor Iv, relating pile-head motion and free-field soil surface motion, a dimensionless strain transmissibility factor Iε, relating pile and soil peak normal strains, and a pile-to-pile interaction factor α measuring group effects. It is shown that a pile foundation may significantly reduce the vertical seismic excitation transmitted to the base of a structure.     

Experimental Investigation of the Reinstallation of Spudcan Footings Close to Existing Footprints

The large footprints that remain on the seabed after offshore mobile jack-up platforms have completed operations provide hazardous conditions for any future jack-up installation at that site. The slope of the footprint and varying soil strengths below the surface cause detrimental horizontal and moment loads to be induced on the spudcan during the preloading process where only vertical loads are expected. Experimental data from 12 tests investigating the reinstallation of a spudcan footing close to an existing footprint is presented in this paper. The experiments were carried out using a geotechnical drum centrifuge at a radial acceleration level equivalent to 250 times that of Earth’s gravity. The stiffness of the loading leg and model spudcan shape were scaled to ensure conditions of stress similitude between the model and prototype. In all of the experiments, an initial footprint was created. The spudcan was then offset and reinstalled with the combined vertical, horizontal, and moment loads on the spudcan recorded. The effects of reinstallation location, preloading levels, and change in leg stiffness were investigated. The worst location for reinstallation was found to be at an offset half a spudcan diameter from the initial spudcan installation. The horizontal and moment loads were also greater when a more extensive footprint was created by the initial spudcan being embedded deeper and with a higher preload. For the range of conditions tested, changing the leg stiffness did not affect the results.     

Three-Dimensional Analysis of Performance of Laterally Loaded Sleeved Piles in Sloping Ground

Development of urban cities in hilly terrain often involves the construction of high-rise buildings supported by large diameter piles on steep cut slopes. Under lateral loads, the piles may induce slope failure, particularly at shallow depths. To minimize the transfer of lateral load from the buildings to the shallow depths of the slope, an annulus of compressible material, referred to as sleeving, is usually constructed between the piles and the adjacent soil. However, the influence of the sleeving on the pile performance in a sloping ground is not fully studied and understood. To investigate the influence, a 3D numerical analysis of sleeved and unsleeved piles on a cut slope is described in this paper. The influences of relative soil stiffness on the response of sleeved piles are also examined. The load transfer from the laterally loaded sleeved pile to the sloping ground is primarily through a shear load transfer mechanism in the vertical plane. Under small lateral loads, the sleeving can lead to a significant reduction in subgrade reaction on the sleeved pile segment and may considerably increase the pile deflection and bending moments. Under large lateral loads, the influence of the sleeving on pile performance appears to diminish because of the widespread plastic zones developed around the pile.