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.     

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.     

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.     

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 Response Adjacent to Braced Excavation

The excavation of soil for the construction of basements or cut-and-cover tunnels results in ground movements. One particular concern is that the excavation-induced lateral soil movements may adversely affect any nearby pile foundation. The lateral loads imposed by the soil movements induce bending moments and deflections in the pile, which may lead to structural distress and failure. This paper presents the results of an actual full-scale instrumented study that was carried to examine the behavior of an existing pile due to nearby excavation activities resulting from the construction of a 16 m deep cut-and-cover tunnel. The pile was located 3 m behind a 0.8 m thick diaphragm wall. Excavation to the formation level that was 16 m below the ground surface resulted in a maximum lateral pile movement of 28 mm. A simplified numerical procedure based on the finite-element method was used to analyze the pile response. Generally, the theoretical predictions were in reasonable agreement with the measured results.     

Pseudostatic Approach for Seismic Analysis of Single Piles

This paper evaluates a simple approximate methodology for estimating the maximum internal forces of piles subjected to lateral seismic excitation. The method involves two main steps: computation of the free-field soil movements caused by the earthquake and the analysis of the response of the pile to the maximum free-field soil movements (considered as static movements) plus a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. The applicability of this approach has been verified by an independent benchmark analysis developed by the writers. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment and shear. The methodology is then used to obtain the response of the Ohba-Ohashi bridge in Japan to one of the earthquakes that occurred in the 1980s. Good agreement is found between the computed and measured pile moments.     

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.     

Raked Piles—Virtues and Drawbacks

This technical note examines some of the characteristics of behavior of pile groups containing raked piles, via a simplified and hypothetical example. Three cases are examined: (1) a group subjected to vertical and lateral loadings, with no ground movements; (2) a group subjected to vertical and lateral loadings, but with vertical ground movements also acting on the group; and (3) a group subjected to vertical and lateral loadings, but with horizontal ground movements acting on the group. In each case, the effect of pile rake on typical behavioral characteristics (group settlement, lateral deflection and rotation, and pile loads and moments) are examined. It is found that, while the presence of raked piles can provide some advantages when the group is subjected to applied vertical and lateral loadings, especially in relation to a reduction in lateral deflection, some aspects of group behavior may be adversely affected when either vertical or horizontal ground movements act on the group. Thus, caution must be exercised in employing raked piles when such ground movements are expected to occur.     

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.     

Behavior of Driven Ultrahigh-Performance Concrete H-Piles Subjected to Vertical and Lateral Loadings

In the United States, an estimated $1 billion is spent annually on repair and replacement of deep foundations. In a recent study, the possibility of using ultrahigh-performance concrete (UHPC) for deep foundation applications was explored with the objectives of increasing the service life of deep foundations supporting bridges to 75 years and reducing maintenance costs. This paper focuses on field evaluation of two UHPC piles and references a steel H-pile. An UHPC pile with an H shape was designed to simplify the process of casting the pile and reduce the volume (i.e., cost) of the material needed to cast the pile. Two instrumented UHPC piles were driven in loess on top of a glacial till clay soil and load tested under vertical and lateral loads. This paper provides a complete set of results for the field investigation conducted on UHPC H-shaped piles. The results presented in this paper prove that the designed UHPC piles can be driven using the same equipment used to drive steel H-piles through hard soil layers without a pile cushion. The vertical load capacity of the UHPC pile was over 80% higher than that of the steel H-piles.     

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.     

Lateral Behavior of Pile Groups in Layered Soils

Assessment of the response of a laterally loaded pile group based on soil–pile interaction is presented in this paper. The behavior of a pile group in uniform and layered soil (sand and/or clay) is evaluated based on the strain wedge model approach that was developed to analyze the response of a long flexible pile under lateral loading. Accordingly, the pile’s response is characterized in terms of three-dimensional soil–pile interaction which is then transformed into its one-dimensional beam on elastic foundation equivalent and the associated parameter (modulus of subgrade reaction Es) variation along pile length. The interaction among the piles in a group is determined based on the geometry and interaction of the mobilized passive wedges of soil in front of the piles in association with the pile spacing. The overlap of shear zones among the piles in the group varies along the length of the pile and changes from one soil layer to another in the soil profile. Also, the interaction among the piles grows with the increase in lateral loading, and the increasing depth and fan angles of the developing wedges. The value of Es so determined accounts for the additional strains (i.e., stresses) in the adjacent soil due to pile interaction within the group. Based on the approach presented, the p–y curve for different piles in the pile group can be determined. The reduction in the resistance of the individual piles in the group compared to the isolated pile is governed by soil and pile properties, level of loading, and pile spacing.     

Permanent Strains of Piles in Sand due to Cyclic Lateral Loads

The strain superposition concept, proposed for ballast study, is applied here to evaluate strain accumulation for laterally loaded piles in sand. It is shown that the soil properties, types of pile installation, cyclic loading types, pile embedded length, and pile∕soil relative stiffness ratio are important factors that influence the pile behavior under mixed lateral loads. These factors are quantified by means of a degradation factor, t, which is derived from the results of 20 full-scale pile load tests and then verified using 6 additional full-scale pile load tests.     

Undrained Lateral Pile Response in Sloping Ground

Three-dimensional finite element analyses were performed to study the behavior of piles in sloping ground under undrained lateral loading conditions. Piles of different diameter and length in sloping cohesive soils of different undrained shear strength and several ground slopes were considered. Based on the results of the finite element analyses, analytical formulations are derived for the ultimate load per unit length and the initial stiffness of hyperbolic p-y curves. New p-y criteria for static loading of piles in clay are proposed, which take into account the inclination of the slope and the adhesion of the pile-slope interface. These curves are used through a commercial subgrade reaction computer code to parametrically analyze the effect of slope inclination and pile adhesion on lateral displacements and bending moments. To validate the proposed p-y curves, a number of well documented lateral load tests are analyzed. Remarkable agreement is obtained between predicted and measured responses for a wide range of soil undrained shear strength and pile diameter, length, and stiffness.     

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.     

Combined Finite- and Boundary-Element Analysis of the Effects of Tunneling on Single Piles

An efficient and practical method of analysis to predict the effects of tunneling on existing single pile foundations is described. The method involves a combination of the finite- and boundary-element (FAB) methods, with free-field ground movements predicted by the finite-element method and the response of an embedded pile to these ground movements predicted by the boundary-element method. The method allows prediction of the full three-dimensional (3D) response of the pile as tunnel excavation proceeds towards the pile and away from it. Very good agreement is obtained between predictions of the pile response obtained by the FAB method and a 3D finite-element analysis which specifically includes the pile in the finite-element mesh. The vastly superior computational efficiency of the FAB method over the full 3D finite element approach is also illustrated.     

Inelastic Analysis of Pile–Soil Interaction

In this paper, inelastic pile–soil interaction is analyzed by using a hybrid type of numerical method. Piles are modeled as linear finite elements and the soil half-space is modeled using boundary elements. Inelastic modeling of the soil media is introduced by a rational approximation to a continuum with nonlinear interface springs along the piles. For this purpose, a modified ?zdemir’s nonlinear model is implemented and systems of equations are coupled for piles and pile groups at interacting nodes. To verify the proposed algorithm, three experimental results from previously conducted tests on piles under static axial and lateral loads are compared with those obtained from the present analysis.     

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.     

Application of Periodic Boundary for Large Pile Group

Full-scale testing of a large pile group is economically not feasible. A concept based on a periodic boundary has been used to study lateral behavior of a large pile group. The approach and findings from anchorage design of a major suspension bridge in California are presented here. Using the repeating nature of soil's displacement field within infinite number of piles arranged in a regular grid pattern, soil-pile interaction phenomenon from the finite area enclosed by one periodic soil boundary effectively represents behavior of the entire pile group. A 3D finite-element analysis was used to create the soil-pile models in which the boundary conditions mimic the repeating nature of the infinite number of piles by slaving the boundary nodes. The soil resistance, as calculated from the finite-element method employing the periodic boundary, is compared with the empirical p-y curve approach for a single isolated pile to determine the group effects. Values of p-multiplier and y-multiplier have been obtained for different pile spacings.     

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.