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.     

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.     

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.     

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.     

Analysis of Load Tests on Piles Driven through Calcareous Desert Sands

The ultimate bearing capacity of short, precast concrete piles driven into calcareous sands was examined by pile-load tests carried out at two sites in Kuwait. The piles had a 0.3 m × 0.3 m square cross section and extended to a maximum depth of 12 m. They were driven through a loose-to-compact calcareous surface sand layer underlain by a competent dense-to-very-dense siliceous cemented sand deposit. The pile tips and part of the pile shafts were embedded in the lower layer. The base resistance and shaft friction were calculated using the Meyerhof method for a layered soil profile. The method employs the standard penetration test N values. The results indicate that a great portion of the pile capacity is due to base resistance. The skin friction mobilized is small and consists of two components corresponding to the two layers penetrated along the pile shafts. The calculated pile capacities were very close to the measured values. The unit skin friction is not constant along the pile shafts.     

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.     

Applicability of Conventional p-y Relations to the Analysis of Piles in Laterally Spreading Soil

This paper presents a kinematic analysis of a single pile embedded in a laterally spreading layered soil profile and discusses the relevancy of conventional analysis models to this load case. The research encompasses the creation of three-dimensional (3D) finite-element (FE) models using the OpenSees FE analysis platform. These models consider a single pile embedded in a layered soil continuum. Three reinforced concrete pile designs are considered. The piles are modeled using beam-column elements and fiber-section models. The soil continuum is modeled using brick elements and a Drucker-Prager constitutive model. The soil-pile interface is modeled using beam-solid contact elements. The FE models are used to evaluate the response of the soil-pile system to lateral spreading and two alternative lateral load cases. Through the computation of force density-displacement (p-y) curves representative of the soil response, the FE analysis (FEA) results are used to evaluate the adequacy of conventional p-y curve relationships in modeling lateral spreading. It is determined that traditional p-y curves are unsuitable for use in analyses where large pile deformations occur at depth.     

In Situ Soil Response to Vibratory Loading and Its Relationship to Roller-Measured Soil Stiffness

An investigation was conducted to characterize and relate in situ soil stress-strain behavior to roller-measured soil stiffness. Continuous assessment of soil stiffness via roller vibration monitoring has the potential to significantly advance performance based quality assurance of earthwork. One vertically homogeneous and two layered test beds were carefully constructed with embedded sensors for the field testing program. Total normal stress and strain measurements at multiple depths reveal complex triaxial soil behavior during vibratory roller loading. Measured cyclic strain amplitudes were 15–25% of those measured during static roller passes due to viscoelasticity and curved drum/soil interaction. Low amplitude vibratory roller loading induces nonlinear in situ modulus behavior. Roller-measured stiffness and its dependence on excitation force is influenced by the stress-dependent modulus function of each soil, the varying drum/soil contact area, and by layer characteristics (modulus ratio, thickness) when layering is present. On vertically homogeneous clayey sand, roller-measured stiffness decreased with increasing excitation force, a behavior attributed to stress-dependent modulus reduction observed in situ. On the crushed rock over silt test bed, roller-measured stiffness increased with increasing excitation force despite the mild stress-dependent modulus reduction observed in the crushed rock. In this case, the stiffer crushed rock takes on a greater portion of the load, resulting in the increase in roller-measured stiffness.     

Estimation of Maximum Liquid Depth in Layered Drainage Blankets over Landfill Barriers

Based on an extended form of the Dupuit assumption, this technical note proposes a computational solution for calculating the maximum liquid depth (Dmax) in layered porous media (e.g., geosynthetic and/or soil drainage blankets of landfills) under free discharge condition. The liquid profile and the location of Dmax for either homogeneous media or layered media can be provided from the approach presented in this technical note. In comparison with the results obtained by application of other methods, the presented approach is verified. Most approaches other than the presented method may lead to considerable error, especially when applied to the drainage system, which consists of a drainage geocomposite overlain by a sand layer with low hydraulic conductivity. The variations of Dmax in two-layered drainage media with varying geometrical parameters and varying hydraulic properties are studied by a parametric analysis. The results demonstrate for a medium consisting of two sand layers, if the hydraulic conductivity of the upper layer is smaller than that of the lower layer and the maximum liquid thickness above the barrier exceeds the thickness of the lower layer, Dmax is very sensitive to the hydraulic conductivity of the upper layer. For a medium consisting of a drainage geocomposite overlain by a sand layer, Dmax is significantly influenced by inflow rate, transmissivity of the geocomposite, and the hydraulic conductivity of the sand when they are not extraordinarily low, and Dmax is much more sensitive to the slope of the drainage layer compared with the system consisting of two sand layers. It is of great advantage to increase the inclination when geocomposites are applied as drainage material.     

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.     

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.     

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

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

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.     

Modeling Lateral Soil-Pile Response Based on Soil-Pile Interaction

Although most designers prefer the p-y curve method as compared to elastic continuum or finite-element analysis of laterally loaded pile behavior, the profession has reached a state where it is time that closer scrutiny be given to the traditional “Matlock-Reese” p-y curves used in the analysis. The traditional p-y curves were derived from a number of well-instrumented field tests that reflect a limited set of conditions. To consider these p-y curves as unique is questionable. As important as such curves have been to advancing the practice from elastic to nonlinear beam on elastic foundation analysis, such calibrated∕verified p-y curves reflect the specific field test conditions (particularly the pile properties) encountered. As presented in this paper, there are additional influences such as pile bending stiffness, pile cross-sectional shape, pile-head fixity, and pile-head embedment that have an effect on the resulting p-y curves. It is argued that strain wedge (SW) model formulation can be used to characterize such effects. SW model analysis predicts the response of laterally loaded piles and has shown very good agreement with actual field tests in sand, clay, and layered soils. The advantage of the SW model is that it is capable of taking into account the effect of changes in soil and pile properties on the resulting p-y curves.     

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).     

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.     

Soil Moisture Flow Modeling with Water Uptake by Plants (Wheat) under Varying Soil and Moisture Conditions

A variably saturated soil moisture flow model is developed for planted soils with depth varying properties by incorporating a nonuniform macroscopic root water uptake function. The model includes spatial and temporal variation of the root density with dynamic root growth for simulating water uptake by plants along with the impact of soil moisture availability. The governing partial differential moisture flow equation integrated over the depth with a plant water uptake term is solved numerically by the implicit finite difference method using an iterative scheme. The model is first tested for barren soils for two profiles considering constant and depth varying soil characteristics under constant inflow condition. The results obtained are later tested with experimental data available in the literature. A nonuniform plant water uptake term is subsequently incorporated in the model and water uptake by wheat plants under different soil moisture availability conditions is studied. Finally, the moisture flow model is validated with field data of rain fed wheat (Triticum aestivum) using a dynamic root growth model for a layered root zone soil profile. The simulated soil moisture regime of the layered root zone shows a reasonably good agreement with the observed data.     

Vertically Loaded Single Piles in Gibson Soil

The available closed-form solutions for vertically loaded piles have been, strictly speaking, limited to homogeneous soil, or nonhomogeneous soil with the shear modulus as a power of depth. The latter solutions—based on a zero shear modulus at ground surface—are generally sufficiently accurate for normally consolidated soil. For overconsolidated soil, however, there is generally a nonzero shear modulus at the surface, which may affect pile response. In this note, rigorous closed-form solutions are established to account for the nonhomogeneity of soil profile with nonzero shear modulus at ground surface. The solutions are developed using a load transfer approach, and are shown to give satisfactory results in comparison with a more rigorous continuum-based numerical approach, when the proposed load transfer factors are adopted.     

Nonlinear Interaction of Soil–Pile in Horizontal Vibration

This paper presents a new model for analyzing a nonlinear soil–pile interaction subject to horizontal shaking of a vertical circular pile embedded in a soil layer of finite thickness. The pile rests on bedrock with either a pinned or a clamped support. The soil mass is assumed composing of a “semi-nonlinear” inner soil zone around the pile and a linear viscoelastic soil zone outside the inner zone. When the inner soil behaves linearly, the present solutions are identical to those obtained by Nogami and Novak in 1977. Numerical results show that soil resistance of less slender piles developed against the vibration is larger than that of more slender piles. Soil resistance depends more strongly on the size of the nonlinear inner zone when the pile is vibrating at a frequency higher than the natural frequency of the soil. Soil nonlinearity, in general, results in a smaller damping and stiffness of the soil–pile system, except at high frequency. At higher vibration frequency, the situation can be very complicated. The exact value of the dynamic stiffness of the soil–pile system depends on elastic shear wave speed, soil nonlinearity, vibration frequency, slenderness ratio of the pile, magnitude of vibration, and tip conditions of the pile. Generally speaking, the dynamic stiffness is smaller than the static stiffness. The normalized dynamic stiffness for pile with a pinned tip is, in general, larger than that with a clamped tip, while the reverse is true for the damping.     

Pile Response to Lateral Spreads: Centrifuge Modeling

The paper presents results of eight centrifuge models of vertical single piles and pile groups subjected to earthquake-induced liquefaction and lateral spreading. The centrifuge experiments, conducted in a slightly inclined laminar box subjected to strong in-flight base shaking, simulate a mild, submerged, infinite ground slope containing a 6-m-thick prototype layer of liquefiable Nevada sand having a relative density of 40%. Two- and three-layer soil profiles were used in the models, with a 2-m-thick nonliquefiable stratum placed below, and in some cases also above the liquefiable Nevada sand. The model piles had an effective prototype diameter, d, of 0.6 m. The eight pile models simulated single end-bearing and floating reinforced concrete piles with and without a reinforced concrete pile cap, and two 2×2 end-bearing pile groups. Bending moments were measured by strain gauges placed along the pile models. The base shaking liquefied the sand layer and induced free field permanent lateral ground surface displacements between 0.7 and 0.9 m. In all experiments, the maximum permanent bending moments, Mmax occurred at the boundaries between liquefied and nonliquefied layers; the prototype measured values of Mmax ranged between about 10 and 300 kN?m. In most cases the bending moments first increased and then decreased during the shaking, despite the continued increase in free field displacement, indicating strain softening of the soil around the deep foundation. The largest values of Mmax were associated with single end-bearing piles in the three-layer profile, and the smallest values of Mmax were measured in the end-bearing pile groups in the two-layer profile. The companion paper further analyzes the Mmax measured in the single pile models, and uses them to calibrate two limit equilibrium methods for engineering evaluation of bending moments in the field. These two methods correspond to cases controlled, respectively, by the pressure of liquefied soil, and by the passive pressure of nonliquefied layers on the pile foundation.