Employment of the P-Multiplier in Pile-Group Analysis

This paper discusses the variation of the P-multiplier (Pm) used with the p-y curve to assess the response of a pile group under lateral loads, which is a crucial topic for the design of bridge pile foundations. Pm is influenced by the site geotechnical conditions (i.e., soil profile, type and properties), pile front and side spacings, and pile-group deflection. The presented study shows the needs to incorporate these factors with the recommended sets of Pm to avoid any compromise or uncertainty when Pm is treated as a single (unique) value based only on pile spacings. The current study addresses these influential elements using the strain wedge (SW) model technique, suggested Pm values, and data collected from full-scale pile-group load tests. The experimental results show that Pm is not unique and must be assessed based on the site geotechnical conditions along with the pile-row front and side spacings. Because the employed Pm values must be a function of these influential factors, additional full- and model-scale load tests with different pile spacings and soil types might be required. The paper also emphasizes that using other techniques, such as the SW model, in addition to the P-multiplier could increase the confidence in the predicted pile-group lateral response.     

Vertical Vibration of Full-Scale Pile—Analytical and Experimental Study

This paper presents the results of vertical vibration tests on two full-scale single piles. The diameter of pile and embedded depth were 0.45 and 22 m, respectively. The soil samples were collected from three boreholes located at the site of investigation and it was explored to a depth up to 30.45 m below the ground level. The vertical vibration tests were conducted for different eccentricities to determine the frequency-amplitude response of the pile. Static load tests were also carried out on two single piles. A simple axisymmetric two-dimensional finite-element model was developed to predict the dynamic pile response. Novak’s plane strain model was also used for the prediction of the dynamic response of single pile. It was observed that the finite-element model predicted the natural frequency and peak displacement amplitude of pile reasonably well. However, prediction of dynamic response of the pile was found unsatisfactory by Novak’s plane strain model. Possible reasons for unsatisfactory performance of Novak’s model were investigated and presented.     

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.     

Experimental Evaluation of Lateral-Load Resistance of Pile Caps

Although pile caps have considerable ability to resist lateral loads, this resistance is often neglected in design. Published cases involving a variety of pile and cap sizes, soil conditions, and loading conditions indicate that the lateral-load resistance of pile caps can be significant, but it is difficult to generalize on the basis of these results because of the variations in conditions involved in the tests. To develop a more systematic basis for evaluating cap resistance, a field test facility was constructed to perform full-scale lateral-load tests on single piles and pile groups, with the pile caps embedded in the stiff natural soil at the site and with the pile caps backfilled with granular soil. Thirty-one tests were conducted to evaluate the lateral-load resistance of pile caps by comparing the response of pile groups with caps fully embedded and with soil removed from around the caps. The results of the tests show that pile caps provide significant resistance to lateral load. This resistance depends primarily on the stiffness and strength of the soil in front of the cap and the depth of cap embedment.     

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.     

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.     

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.     

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.     

Estimation of Load Capacity of Pipe Piles in Sand Based on Cone Penetration Test Results

Pipe piles can be classified as either closed- or open-ended piles. In the present paper, the load capacity of both closed- and open-ended piles is related to cone penetration resistance qc through an experimental program using calibration chamber model pile load tests and field pile load tests. A total of 36 calibration chamber pile load tests and two full-scale field pile load tests were analyzed. All the test piles were instrumented for separate measurement of each component of pile load capacity. Based on the test results, the normalized base resistance qb/qc was obtained as a function of the relative density DR for closed-ended piles, and of both the relative density DR and the incremental filling ratio (IFR) for open-ended piles. A relationship between the IFR and the relative density DR is proposed as a function of the pile diameter and driving depth. The relationship between IFR and DR allows the estimation of IFR and thus of the pile load capacity of open-ended piles at the design stage, before pile driving operations.     

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.     

Construction Effect on Load Transfer along Bored Piles

The load transfer behavior along bored piles is affected by details of pile construction particularly those imposing stress and moisture changes to the surrounding soils. An investigation involving moisture migration tests, in situ horizontal stress measurements, and borehole shear and pressuremeter tests shows clear effects of construction that lead to subsequent changes in soil properties. The construction of bored piles in Singapore and the region often involves casting of concrete either in unsupported “dry” boreholes or in “wet” boreholes filled with water. It is necessary to differentiate these two extreme construction conditions in bored pile design. Based on triaxial compression and pressuremeter tests on the residual soil of the Jurong Formation in Singapore, the variation of soil modulus with shear strain can be described by a hyperbolic function. A procedure is recommended for assessing the combined effect of stress relief and soaking on soil modulus by introducing a modulus reduction factor. Modulus degradation curves from pressuremeter tests with the borehole conditions properly simulated are found capable of producing load transfer curves that are comparable to those deduced in the field.     

Lateral Response Evaluation of Single Piles Using Inclinometer Data

In an effort to develop an efficient method for interpretation of lateral pile load test results via measured inclinometer data only, an analytical model is proposed based on energy conservation of a pile-soil system. A Fourier series function is used to represent deflection behavior of the pile-soil system. In order to obtain shear, moment, and soil reaction along the pile shaft, convergence of the series after differentiation is guaranteed by applying the Cesaro sum technique. The concrete cracking effect is also incorporated into the pile model to account for yielding of the pile itself. Three full-scale pile load cases are then used to verify the feasibility of the developed methodology as well as make comparison to other methods.     

Behavior of Slender Piles Subject to Free-Field Lateral Soil Movement

Soil movements associated with slope instability induce shear forces and bending moments in stabilizing piles that vary with the buildup of passive pile resistance. For such free-field lateral soil movements, stress development along the pile element is a function of the relative displacement between the soil and the pile. To investigate the effects of relative soil-pile displacement on pile response, large-scale load tests were performed on relatively slender, drilled, composite pile elements (cementitious grout with centered steel reinforcing bar). The piles were installed through a shear box into stable soil and then loaded by lateral translation of the shear box. The load tests included two pile diameters (nominal 115 and 178?mm) and three cohesive soil types (loess, glacial till, and weathered shale). Instrumentation indicated the relative soil-pile displacements and the pile response to the loads that developed along the piles. Using the experimental results, an analysis approach was evaluated using soil p-y curves derived from laboratory undrained shear strength tests. The test piles and analyses helped characterize behavioral stages of the composite pile elements at loads up to pile section failure and also provided a unique dataset to evaluate the lateral response analysis method for its applicability to slender piles.     

Data Reduction of Horizontal Load Full-Scale Tests on Bored Concrete Piles and Pile Groups

This paper proposes a new approach for data reduction of horizontal load full-scale tests on piles and pile groups. This approach has been developed on results from tests run on bored concrete piles embedded in homogeneous and nonhomogeneous ground. Due to nonlinear response of pile material and also to nonhomogeneous embedding ground, the problem of fitting reliable curves for representing strains along shafts is increased. It is suggested that B-splines fixed by a weighted least-squares algorithm should be used to overcome that problem. Taking advantage of the mathematical properties of B-splines, an algorithm for computing the internal force distribution amongst pile heads direct from test results is also proposed for pile groups. It is shown that the integration of the curvatures to compute pile movements should be done using natural boundary conditions instead of pile head measurements whenever possible. Despite the concrete crack, the distribution of bending moments can be computed from curvatures provided a reliable reinforced concrete model is used. Finally, it is proposed to compute the soil reactions by the integration of bending moments, solving an integral equation by again using B-spline functions.     

Load Testing of a Closed-Ended Pipe Pile Driven in Multilayered Soil

Piles are often driven in multilayered soil profiles. The accurate prediction of the ultimate bearing capacity of piles driven in mixed soil is more challenging than that of piles driven in either clay or sand because the mechanical behavior of these soils is better known. In order to study the behavior of closed-ended pipe piles driven into multilayered soil profiles, fully instrumented static and dynamic axial load tests were performed on three piles. One of these piles was tested dynamically and statically. A second pile served as reaction pile in the static load test and was tested dynamically. A third pile was tested dynamically. The base of each pile was embedded slightly in a very dense nonplastic silt layer overlying a clay layer. In this paper, results of these pile load tests are presented, and the lessons learned from the interpretation of the test data are discussed. A comparison is made of the ultimate base and limit shaft resistances measured in the pile load tests with corresponding values predicted from in situ test-based and soil property-based design methods.     

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.     

Assessment of the Axial Load Response of an H Pile Driven in Multilayered Soil

Most of the current design methods for driven piles were developed for closed-ended pipe piles driven in either pure clay or clean sand. These methods are sometimes used for H piles as well, even though the axial load response of H piles is different from that of pipe piles. Furthermore, in reality, soil profiles often consist of multiple layers of soils that may contain sand, clay, silt or a mixture of these three particle sizes. Therefore, accurate prediction of the ultimate bearing capacity of H piles driven in a mixed soil is very challenging. In addition, although results of well documented load tests on pipe piles are available, the literature contains limited information on the design of H piles. Most of the current design methods for driven piles do not provide specific recommendations for H piles. In order to evaluate the static load response of an H pile, fully instrumented axial load tests were performed on an H pile (HP?310×110) driven into a multilayered soil profile consisting of soils composed of various amounts of clay, silt and sand. The base of the H pile was embedded in a very dense nonplastic silt layer overlying a clay layer. This paper presents the results of the laboratory tests performed to characterize the soil profile and of the pile load tests. It also compares the measured pile resistances with those predicted with soil property- and in situ test-based methods.     

Statnamic Damping Coefficient: Numerical Modeling Approach

The damping associated with dynamic or statnamic tests has typically been over simplified to provide a “catch-all” factor for those responses that could not be fully accounted for using present analyses. This factor has historically been considered constant for a given pile–soil system, but recent investigations as well as previous case studies show the plausibility of another explanation. This study hypothesizes that damping is more closely associated with the increase in strain and not the total strain. Therein, the change in the volumetric strain is being scrutinized to investigate its relationship to damping. To validate this assumption, a numerical model is created which simulates the testing of a full-scale drilled shaft and results analyzed to determine the extent of the zone of influence and volumetric contribution to damping.     

Nonlinear Analysis of Torsionally Loaded Piles in a Two-Layer Soil Profile

This paper presents a method for predicting the nonlinear response of torsionally loaded piles in a two-layer soil profile, such as a clay or sand layer underlain by rock. The shear modulus of the upper soil is assumed to vary linearly with depth and the shear modulus of the lower soil is assumed to vary linearly with depth and then stay constant below the pile tip. The method uses the variational principle to derive the governing differential equations of a pile in a two-layer continuum and the elastic response of the pile is then determined by solving the derived differential equations. To consider the effect of soil yielding on the behavior of piles, the soil is assumed to behave linearly elastically at small strain levels and yield when the shear stress on the pile-soil interface exceeds the corresponding maximum shear resistance. To determine the maximum pile-soil interface shear resistance, methods that are available in the literature can be used. The proposed method is verified by comparing its results with existing elastic solutions and published small-scale model pile test results. Finally, the proposed method is used to analyze two full-scale field test piles and the predictions are in reasonable agreement with the measurements.     

Reduction Factor for the Unloading Point Method at Clay Soil Sites

Full-scale testing can be an integral component of quality control/quality assurance for projects involving construction of deep foundations. Rapid load tests are being used in the deep foundation industry as a method for assessing the axial static behavior of deep foundations. Since rapid load tests involve dynamics, inertial and damping forces must be considered in analyzing measured pile response to estimate the static pile response. The unloading point method (UPM) is typically used for this purpose. Generally considered a consequence of load rate effects in clays, results from the UPM must be further modified by a reduction factor to obtain a reasonable estimate of the static pile response. A reduction factor of 0.65 applied to the UPM for clay soil sites has been recommended by others. However, a review and analysis of readily available literature reporting static and rapid pile load test results at sites predominantly consisting of clay soils indicate that an average reduction factor of 0.47 is more appropriate. Rapid load testing should be used judiciously. When using the UPM to estimate static pile capacity from rapid load tests in clay, static load tests should be performed to validate the reduction factor used to interpret rapid load tests.