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.     

Rotational Restraint of Pile Caps during Lateral Loading

A pure fixed-head (zero-rotation) condition at the top of a group of laterally loaded piles is seldom achievable in the field, even when piles are installed in a group that is “rigidly” constrained by a stiff concrete pile cap. Assuming complete fixity during design (zero rotation at the pile head) can result in underestimated values of pile-head deflection, and incorrect estimates of the magnitude and the location of maximum bending moments. A simple and practical approach is presented for estimating the moment restraint that is provided by the pile cap at the top of a pile group. The moment restraint, represented by the rotational restraint coefficient (KMθ), serves as a boundary condition for analyzing groups of laterally loaded piles. Full-scale field tests performed on two pile groups with concrete pile caps show that the proposed method for estimating rotational restraint provides results that are in good agreement with measured field performance.     

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.     

Practical Solution for Group Stiffness Analysis of Piles

This paper presents a practical solution for group stiffness estimate of vertically loaded piles. The solution is based on a variational approach for pile groups in a soil modeled using a load–transfer curve method. Using the present method, the group stiffness of piles can be easily obtained based on spreadsheet calculation and this is very useful for practical purpose. The paper also presents comparison between results from modeling the soil using load–transfer curves and as an elastic half space. Their difference in estimating the group stiffness of piles is addressed.     

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.     

Analytical Solution for Piles Supporting Combined Lateral Loads

Analytical solutions of normalized maximum deflection and normalized maximum moment for laterally loaded long piles in homogeneous elastoplastic soil under combined loads are presented in this paper. Both the normalized deflection surface and normalized moment surface are continuous and increasing constantly with normalized applied force and moment with various slopes. It shows that the normalized applied force and moment have different contributions to the deflection and moment. In general, the variation of normalized moment surface is relatively moderate compared to normalized maximum deflection. Due to the nonlinear effect, the deflections and moments using superposition approach will be on the unsafe side. The analytical solutions can be used for any elastic materials, any type of soil, and any shapes of pile cross section. Above all, the analytical solutions may be easily applied to calculate the maximum deflection or moment of lateral long piles subject to combined loads accurately using a calculator.     

Laterally Loaded Pile Study in Permafrost of Northern Québec, Canada

This paper describes a study undertaken at Umiujaq, in northern Québec, on laterally loaded piles in permafrost subject to a constant displacement rate. Test results of bending moments, shear load, soil reaction, and pile displacements demonstrate the complex nature of creep of frozen soils. FEM simulations show a good concurrence with field test results and confirm a clear distinction between stationary and nonstationary creep.     

Reliability Analysis of Laterally Loaded Piles Involving Nonlinear Soil and Pile Behavior

An alternative approach of analyzing laterally loaded piles in the ubiquitous spreadsheet platform is presented. The numerical procedure couples nonlinear pile flexural rigidity (EpIp) with nonlinear p-y analysis. The deterministic study is then extended to carry out reliability analysis, which reflects the uncertainties and correlation structure of the underlying parameters. The reliability index is evaluated based on the alternative intuitive perspective of an expanding equivalent ellipsoid in the original space of the random variables. This paper investigates two modes of failure: deflection and bending moment, and considers non-normal random variables. Spatial variability of the soil medium is accounted for by incorporating an autocorrelation model. The spreadsheet-based reliability approach can also be coupled with stand-alone programs via the response surface method. The probabilities of failure inferred from reliability indices agree well with Monte Carlo simulations. Simple reliability-based design is demonstrated, in which the appropriate pile section or length that satisfies target reliability in one or more limit states is sought.     

Free-Field Measurements to Disclose Lateral Reaction Mechanism of Piles Subjected to Soil Movements

Soil-pile interaction remains to be the most ambiguous yet one of the most crucial aspects in the design of laterally loaded soil-pile systems subjected to embankment-induced movements. This paper proposes a new method that is capable of producing soil stiffness degradation curves, which are the outcome of real field behavior through free-field measurements. Soil-pile interaction mechanism can be solved with the proposed method for any possible case either the piles are constructed before the embankment construction or during and after. For any time considered, the method enables the computation of resultant stress effects on the pile cross section and the accompanying deflections. To provide a basis of comparison, an example problem has been solved with the proposed method and with two well-known commercial finite-element softwares. Obtained results indicated the capability of the proposed method to disclose real field behavior, which can be attributed to its inherent property of being also an observational method.     

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.     

Wedge Failure Analysis of Soil Resistance on Laterally Loaded Piles in Clay

A fundamental study of pile-soil systems subjected to lateral loads in clay soil was conducted by using experimental tests and a lateral load-transfer approach. The emphasis was on an improved wedge failure model developed by considering three-dimensional combination forces and a new hyperbolic p-y criterion. A framework for determining the p-y curve on the basis of both theoretical analysis and experimental load test results is proposed. The proposed p-y method is shown to be capable of predicting the behavior of a large-diameter pile under lateral loading. The proposed p-y curves with an improved wedge model are more appropriate and realistic for representing a pile-soil interaction for laterally loaded piles in clay than the existing p-y method.     

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.     

Liquefaction-Induced Settlement of Pile Groups in Liquefiable and Laterally Spreading Soils

The results of a series of dynamic centrifuge tests on model pile groups in (level) liquefied and laterally spreading soil profiles are presented. The piles are axially loaded at typical working loads, which has enabled liquefaction-induced settlements of the foundations to be studied. The development of excess pore pressures within the bearing layer (dense sand) was found to lead to a reduction in pile capacity and potentially damagingly large coseismic settlements. As the excess pore pressure increased, these settlements were observed to exceed postshaking downdrag-induced settlements, which occur due to the reconsolidation of liquefied sand around the pile shaft. In resisting settlement, the pile cap was found to play an important role by compensating for the capacity lost by the piles. This was shown to be achieved by the development of dilative excess pore pressures beneath the pile cap within the underlying loose liquefied sand which provide increasing bearing capacity with settlement. The centrifuge test data show good qualitative and quantitative agreement with the limited amount of model and full-scale data currently available in the literature. The implications of settlement for the design of piled foundations to serviceability conditions in both level and sloping ground are discussed, with settlement becoming an increasingly important consideration for laterally stiffer piles. Finally, empirical relationships have been derived from the test data to relate suitable static safety factors to given increases in excess pore pressure in the bearing layer within a performance-based design framework (i.e., based on limiting displacements).     

Experimental Load–Transfer Curves of Laterally Loaded Piles in Nak-Dong River Sand

This paper describes the results of a model testing of the piles embedded in Nak-Dong River sand, located in south Korea, under monotonic lateral loadings. A number of features were studied, including the lateral resistance of piles, the effect of the installation method, and the pile head restraint condition. The study has led to recommendations of the load–transfer curves (p–y curves) for laterally loaded piles. Modification factors were developed to allow for both a different pile installation method and different pile head restraint conditions by comparison to existing model load tests. The proposed p–y curves were compared to the existing curves and were evaluated with the experimental data. The ultimate lateral soil resistance and subgrade modulus were investigated and discussed. It is revealed that the proposed p–y curves show significant differences in shapes and magnitudes when compared with existing p–y curve models. The accuracy of the proposed p–y curve model, considering the effect of installation method and pile head restraint condition, is very reasonable as shown by comparing measured and predicted lateral behavior of the pile.     

Theoretical p-y Curves for Laterally Loaded Single Piles in Undrained Clay Using Bezier Curves

An alternative method was introduced for predicting the nonlinear p-y curves for monotonic unidirectional laterally loaded single piles in uniform undrained clay. On the basis of numerical studies, closed-form solutions were developed for locating the start of yield (ye); the ultimate yield point (yu); and the initial stiffness, Ki of the p-y curve. The nonlinear section of the curve between the start of the yield and the ultimate yield point was represented by Bezier polynomials (also known as de Casteljau’s algorithm). Using these relationships, a direct method of constructing the p-y curves was presented considering either tension failure or no tension failure of soils. For a typical pile configuration, the resulting load-deflection response was observed to compare favorably with the predictions from FLAC analysis and Matlock.     

Lateral Resistance of Short Single Piles and Pile Groups Located Near Slopes

Many transmission towers, high-rise buildings, and bridges are constructed near steep slopes and are supported by large-diameter piles. These structures may be subjected to large lateral loads, such as violent winds and earthquakes. Widely used types of foundations for these structures are pier foundations, which have large diameter with high stiffness. The behavior of a pier foundation subjected to lateral loads is similar to that of a short rigid pile, because both elements seem to fail by rotation developing passive resistance on opposite faces above and below the rotation point, unlike the behavior of a long flexible pile. This paper describes the results of several numerical studies performed with a three-dimensional finite-element method (FEM) of model tests and a prototype test of a laterally loaded short pile and pier foundation located near slopes, respectively. Initially, in this paper, the results of model tests of single piles and pile groups subjected to lateral loading, in homogeneous sand with 30° slopes and horizontal ground were analyzed by the three- dimensional (3D) finite-element (FE) analyses. Furthermore, field tests of a prototype pier foundation subjected to lateral loading on a 30° slope was reported. The FE analyses were conducted to simulate these results. The main purpose of this paper is the validation of the 3D elasto–plastic FEM by comparisons with the experimental data.     

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.     

Effects of Construction on Laterally Loaded Pile Groups

Full-scale lateral load tests on a group of bored and a group of driven precast piles were carried out as part of a research project for the proposed high-speed rail system in Taiwan. Standard penetration tests, cone penetration tests (CPT), and Marchetti Dilatometer tests (DMT) were performed before the pile installation. The CPT and DMT were also conducted after pile installation. Numerical analyses of the laterally loaded piles were conducted using p-y curves derived from preconstruction and postconstruction DMT and by applying the concept of p multipliers. Comparisons between preconstruction and postconstruction CPT and DMT data and evaluation of the results of computations show that the installation of bored piles softened the surrounding soil, whereas the driven piles caused a densifying effect.     

Centrifuge Model Study of Laterally Loaded Pile Groups in Clay

A series of centrifuge model tests has been conducted to examine the behavior of laterally loaded pile groups in normally consolidated and overconsolidated kaolin clay. The pile groups have a symmetrical plan layout consisting of 2, 2×2, 2×3, 3×3, and 4×4 piles with a center-to-center spacing of three or five times the pile width. The piles are connected by a solid aluminum pile cap placed just above the ground level. The pile load test results are expressed in terms of lateral load–pile head displacement response of the pile group, load experienced by individual piles in the group, and bending moment profile along individual pile shafts. It is established that the pile group efficiency reduces significantly with increasing number of piles in a group. The tests also reveal the shadowing effect phenomenon in which the front piles experience larger load and bending moment than that of the trailing piles. The shadowing effect is most significant for the lead row piles and considerably less significant for subsequent rows of trailing piles. The approach adopted by many researchers of taking the average performance of piles in the same row is found to be inappropriate for the middle rows, of piles for large pile groups as the outer piles in the row carry significantly more load and experience considerably higher bending moment than those of the inner piles.     

Increasing the Resistance of Piles Subject to Cyclic Lateral Loading

Small-scale tests were carried out on a monopile and fin piles to determine the effect the length of fins had upon the lateral displacement of cyclically loaded piles. A variety of loading conditions were applied to model piles in a dense sand by using a mechanical loading system. Ten thousand cycles were used in each test to represent 20 years of environmental loading on offshore structures. Variables included the magnitude, frequency, and direction of the load; the type of pile tip; and the length of the fins. The reduction in pile head displacement was used as a measure of the efficiency of the fins. The tests show that the fins reduced the lateral displacement by at least 50% after 10,000 cycles.