Estimating Subgrade Reaction Modulus for Transversely Isotropic Rock Medium

Most of the rock medium possesses intrinsic grain orientation or preferred bedding and joint directions, thus requiring the use of at least transverse isotropy to describe its elastic behavior. This paper presents a series of charts, based on extensive finite element parametric studies along with nonlinear regression analysis of FE simulation results, for estimating the subgrade reaction modulus (or initial tangent to the p-y curve) using five elastic constants of a transversely isotropic rock mass. The proper characterization of subgrade reaction modulus is critical for accurate prediction of the elastic lateral deflection of a rock socketed drilled shaft under the applied lateral loads. The sensitivity of the response of a laterally loaded drilled shaft to the degree of anisotropy and orientation of the plane of anisotropy (bedding plane direction of the rock medium) was demonstrated in this paper for an actual lateral load testing case in Ohio. It is highly recommended to use five elastic constants to estimate subgrade reaction modulus of rock medium exhibiting high degree of cross anisotropy.     

Lateral Load Capacity of Drilled Shafts in Jointed Rock

Large vertical (axial) and lateral loads often act on the heads of drilled shafts in jointed rock. In current design practice, the p-y curve method used in design of laterally loaded drilled shafts in soil is often also used for shafts in jointed rock. The p-y curve method treats the soil as a continuum, which is not appropriate in jointed rock, particularly when failure occurs due to sliding on joints. A new discontinuum model was developed to determine the lateral load capacity of drilled shafts or piers in a jointed rock mass with two and three joint sets. It consists two parts: a kinematic and a kinetic analysis. In the kinematic analysis, Goodman and Shi’s block theory is expanded to analyze the removability of a combination of blocks laterally loaded by a pier. Based on the expanded theory, a method was developed to select removable combinations of blocks using easily constructed two-dimensional diagrams. In the kinetic analysis, each kinematically selected removable combination of blocks is examined with the limit equilibrium approach to determine the ultimate lateral load capacity. Although the procedure is similar to slope stability analysis, it is more complicated with the addition of a lateral force and the vertical load exerted by the pier. Simple analytical relations were developed to solve for the ultimate lateral load capacity.     

Case History Evaluation of Laterally Loaded Piles

This paper examines seven case histories of load tests on piles or drilled shafts under lateral load. Since the current design software to estimate lateral load resistance of deep foundations requires p-y curves. The first approach used was correlative whereby soil parameters determined from in situ tests [standard penetration test (SPT) and cone penetration test (CPT)] were used as input values for standard p-y curves. In the second approach p-y curves were calculated directly from the stress deformation data measured in dilatometer (DMT) and cone pressuremeter tests. The correlative evaluation revealed that, on the average, predictions based upon the SPT were conservative for all loading levels, and using parameters from the CPT best predicted field behavior. Typically, predictions were conservative, except at the maximum load. Since traditionally SPT and CPT correlation-based p-y curves are for “sands” or “clays,” this study suggests that silts, silty sands, and clayey sands should use cohesive p-y curves. For the directly calculated curves, DMT derived p-y curves predict well at low lateral loads, but at higher load levels the predictions become unconservative. p-y curves derived from pressuremeter tests predicted well for both “sands” and “clays” where pore pressures are not anticipated.     

Relationship between Texas Cone Penetrometer Tests and Axial Resistances of Drilled Shafts Socketed in Clay Shale and Limestone

Modern methods for designing drilled shafts in soft rock require knowledge of the compressive strength and modulus of the rock. However, rock jointing at many sites prohibits the recovery of samples of sufficient length and integrity to test rock cores in either unconfined or triaxial compression tests. Since rational design procedures usually require values of compressive strength, surrogate methods must be employed to estimate the compressive strength of the rock. The surrogate methods considered in this study was Texas cone penetrometer tests, and performed at several sites in North Central Texas. In order to develop the relationships between Texas cone penetrations and side and base resistances of rock socketed drilled shafts, three field load tests were conducted. Based on the field study and literature reviews, a relationship between Texas cone penetration tests and axial resistances of rock socketed drilled shafts was proposed.     

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.     

Nonlinear Analysis of Laterally LoadedRock-Socketed Shafts

In this paper, a nonlinear continuum method is developed to predict the load-displacement response of drilled shafts under lateral loading. The method can consider drilled shafts in a continuum consisting of a soil layer overlying a rock mass layer. The deformation modulus of the soil is assumed to vary linearly with depth, and the deformation modulus of the rock mass is assumed to vary linearly with depth and then to stay constant below the shaft tip. The effect of soil and∕or rock mass yielding on the behavior of shafts is considered by assuming that the soil and∕or rock mass behaves linearly elastically at small strain levels and yields when the soil and∕or rock mass reaction force p (force∕length) exceeds the ultimate resistance pult (force∕length). For the calculation of the ultimate resistance pult of the soil, methods that are available in the literature are used. To calculate the ultimate resistance pult of the rock mass, a method based on the Hoek-Brown strength criterion is proposed. The proposed method is verified by comparing its results with available elastic solutions and field test data, and it is finally applied in the design of a bridge foundation in Massachusetts.     

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.     

Roughness and Unit Side Resistances of Drilled Shafts Socketed in Clay Shale and Limestone

Rock socketed drilled shafts are being used increasingly to support heavily loaded structures. Rock sockets provide resistance to the load through a combination of side and base resistances. In this study, the effect of drilling tools such as an auger and a core barrel on the unit side resistance was investigated. A total of four field studies were performed on clay shale (compressive strength of 1–2?MPa) and limestone (compressive strength of 10?MPa). Borehole roughnesses produced by the different types of drilling tools in clay shale and limestone were measured using a laser borehole roughness profiler developed in this study to measure roughness to 0.5?mm in the boreholes. Based on the results of this study, it was observed that the drilling tools developed different socket roughnesses, which in turn affected the side resistances of the rock socketed drilled shafts.     

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 Method for Load-Transfer Characteristics of Rock-Socketed Drilled Shafts

The load-settlement behavior of rock-socketed drilled shafts under axial loading is investigated by a load-transfer approach. Special attention is given to the shear load-transfer function and an analytical method for estimating load-transfer characteristics of rock-socketed drilled shafts. A nonlinear triple curve is employed to determine the shear load-transfer function of rock-socketed drilled shafts based on the constant normal stiffness direct shear tests and the Hoek-Brown failure criterion. An analytical method that takes into account the soil coupling effect was developed using a modified Mindlin’s point load solution. Through comparisons with field case studies, it is found that the proposed methodology in the present study is in good agreement with the general trend observed by in situ measurements and, thus, represents a significant improvement in the prediction of drilled shaft shear behavior.     

Shear Load Transfer Characteristics of Drilled Shafts in Weathered Rocks

The load distribution and deformation of drilled shafts subjected to axial loads were evaluated by a load-transfer approach. The emphasis was on quantifying the load-transfer mechanism at the interface between the shafts and surrounding highly weathered rocks based on a numerical analysis and on small-scale tension load tests performed on nine instrumented piles. An analytical method that takes into account the soil coupling effect was developed using a modified Mindlin's point load solution. Based on the analysis, a single-modified hyperbolic model is proposed for the shear transfer function of drilled shafts in highly weathered rocks. Through comparisons with field case studies, it is found that the prediction by the present approach is in good agreement with the general trend observed by in situ measurements, and thus represents a significant improvement in the prediction of load deflections of drilled shafts.     

Critical Evaluation of Compression Interpretation Criteria for Drilled Shafts

This paper is a critical evaluation of the interpretation criteria of drilled shafts under axial compression loading. A wide variety of load test data are used for analysis, and these data are divided into drained and undrained databases. The interpretation criteria are examined from these load test results to establish a consistent compression interpretation criterion. Among these criteria, the range of each interpretation method presents approximately the same trend for both drained and undrained conditions. The statistical results show that the smaller the compression displacement, the higher the coefficient of variation. Moreover, the undrained load test results reveal less variability than the drained results. The load-displacement curve of a drained loading also demonstrates more ductility than that for undrained loading. Based on these analyses, the relative merits and interrelationships of these criteria are established, and specific design recommendations for the interpretation of compression drilled shaft load test, in terms of both capacity and displacement, are given.     

Case History: Capacity of a Drilled Shaft in the Atlantic Coastal Plain

This paper presents a single case history of a drilled shaft constructed in the Atlantic Coastal Plain deposits for a bridge foundation that was subjected to axial loading. The predicted nominal axial capacity is estimated based on state of practice empirically derived methods specified in the current AASHTO LRFD Bridge Design Specifications. Predictions are compared to observed soil resistance derived from a static load test conducted on a full-size instrumented test shaft using the Osterberg Cell method. The results suggest that the AASHTO specified prediction methods should be applied cautiously for drilled shafts in the Atlantic Coastal Plain, incorporating an appropriate in situ testing program for evaluating soil design parameters, considering variations from the specific geologic environment and construction methodology used to develop the specified prediction methods, accounting for the load-deformation behavior of the shaft, and providing for instrumented static load testing to measure the actual behavior of the drilled shafts.     

Numerical Study of an Integral Abutment Bridge Supported on Drilled Shafts

The majority of integral abutment bridges (IABs) in the United States are supported on steel H-piles to provide the flexibility necessary to minimize the attraction of large lateral loads to the foundation and abutment. In Hawaii, steel H-piles have to be imported, corrosion tends to be severe in the middle of the Pacific Ocean, and the low buckling capacity of steel H-piles in scour-susceptible soils has led to a preference for the use of concrete deep foundations. A drilled shaft-supported IAB was instrumented to study its behavior during and after construction over a 45-month period. This same IAB was studied using the finite-element method (FEM) in both two- (2D) and three dimensional (3D). The 3D FEM yields larger overall pile curvature and moments than 2D because in 3D, the high plasticity soil is able to displace in between the drilled shafts thereby “dragging” the shafts to a more highly curved profile while soil flow is restricted by plane strain beam elements in 2D. Measured drilled shaft axial loads were higher than the FEM values mainly due to differences between the assumed and actual axial stiffness and to a lesser extent on concrete creep in the drilled shafts and uneven distribution of loads among drilled shafts. Numerical simulations of thermal and stream loadings were also performed on this IAB.     

Influence of Torque on Lateral Capacity of Drilled Shafts in Sands

As a result of recent changes in the requirements involving hurricane extreme events (e.g., wind velocities), the Florida Department of Transportation has moved away from cable-stayed signs, signals, and lights systems to mast arm/pole structures. Unfortunately, the newer systems develop significant lateral and torque loading on their foundations (e.g., drilled shafts). Current design practice for a mast arm/pole foundation is to treat lateral loading and torsion separately (i.e., uncoupled); however, recent field-testing suggests otherwise. This paper reports on the results of 91 centrifuge tests. 54 of the tests were conducted in dry sand and 37, in saturated sands. The tests varied the lateral load to torque ratios, shaft embedment depths, and soil strengths. The experiments revealed that even though the torsional resistances of the shafts were not influenced by lateral load, the shafts’ lateral resistance was significantly impacted by torsion. Reductions in lateral resistance of 50% were recorded for shafts under high torque to lateral load ratios. Using the free earth support assumption and the ultimate soil pressure the soil pressure distribution along the shaft was developed. Using force and moment equilibrium, as well as the applied torque, maximum shear, and moments were computed. The predicted values were found to be within 25% (10% on average, except for the tests in saturated dense sand with polymer slurry) of the experimental results.     

Nonlinear Finite-Element Modeling of Batter Piles under Lateral Load

In this paper, a finite-element model is developed in which the nonlinear soil behavior is represented by a hyperbolic relation for static load condition and modified hyperbolic relation, which includes both degradation and gap for a cyclic load condition. Although batter piles are subjected to lateral load, the soil resistance is also governed by axial load, which is incorporated by considering the P-Δ moment and geometric stiffness matrix. By adopting the developed numerical model, static and cyclic load analyses are performed adopting an incremental-iterative procedure where the pile is idealized as beam elements and the soil as elastoplastic spring elements. The proposed numerical model is validated with published laboratory and field pile test results under both static and cyclic load conditions. This paper highlights the importance of the degradation factor and its influence on the soil resistance-displacement (p-y) curve, number of cycles of loading, and cyclic load response.     

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.     

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.     

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.     

Capacity of Drilled Shafts in Burlington Limestone

Field load tests of three drilled shafts socketed in Burlington limestone were conducted using the Osterberg load cell. The objective of the testing was to compare the load capacities obtained from the field load tests with load capacities predicted using empirical methods. Based on the results of this study, the following conclusions can be drawn. The observed values of unit side resistance exceeded predicted empirical values for two of the three shafts tested (2,343 and 2,278 kPa observed versus 1,550 and 1,252 kPa predicted). However, for one of the shafts, the observed value of unit side resistance was only about ? of the more conservative predicted empirical value (916 kPa observed versus 1,252 predicted). Bearing capacity failure did not occur for two of the three shafts. Bearing capacity failure may have occurred for one of the shafts. Using a factor of safety of 3 applied to the lowest observed value of end bearing pressure implies that the allowable bearing capacity for the Burlington limestone at this site (3 MPa, or ?500 psi) exceeds the typical presumptive bearing capacity for sound limestone in mid-Missouri (1914 kPa or 277 psi).