p-y Criterion for Rock Mass

Drilled shafts socketed in rock mass have been used frequently as a foundation system to support both vertical and lateral loads. Traditionally, the lateral interaction between the drilled shaft and the surrounding rock medium has been characterized by means of nonlinear p-y curves; however, there is a lack of well verified p-y criterion for rock mass. In this paper, a hyperbolic p-y criterion is developed based on both theoretical derivations and numerical (finite element) parametric analysis results. The methods for determining pertinent rock parameters needed for constructing the proposed p-y curves are presented in the paper. Two full-scale lateral load tests on large diameter, fully instrumented drilled shafts socketed in rock conducted by the writers, together with additional four load test results reported by Gabr et al. were used to validate the applicability of the proposed hyperbolic p-y curves for rock mass. The comparisons between the computed shaft responses (both deflections and bending moments) and the actual measured responses are considered acceptable.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Response of Laterally Loaded Large-Diameter Bored Pile Groups

This paper presents results of full-scale lateral load tests of one single pile and three pile groups in Hong Kong. The test piles, which are embedded in superficial deposits and decomposed rocks, are 1.5 m in diameter and approximately 30 m long. The large-diameter bored pile groups consist of one two-pile group at 6 D (D = pile diameter) spacing and one two-pile and one three-pile group at 3 D spacing. This paper aims to investigate the nonlinear response of laterally loaded large-diameter bored pile groups and to study design parameters for large-diameter bored piles associated with the p-y method using a 3 D finite-element program, FLPIER. Predictions using soil parameters based on published correlations and back-analysis of the single-pile load test are compared. It is found that a simple hyperbolic representation of load-deflection curves provides an objective means to determine ultimate lateral load capacity, which is comparable with the calculated values based on Broms' theory. Lateral deflections of bored pile groups predicted using the values of the constant of horizontal subgrade reaction, suggested by Elson and obtained from back-analysis of the single pile load test, are generally in good agreement with the measurements, especially at low loads.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Flexural Performance of Drilled Shafts with Minor Flaws in Stiff Clay

Lateral loads are often the primary forces that act on drilled shafts when they support retaining walls, bridge piers, or building foundations. The construction of drilled shafts often inadvertently introduces flaws that are not always detectable with well-performed nondestructive evaluation (NDE) techniques. The effect of such undetectable minor flaws on the lateral-load performance of drilled shafts needs to be assessed and subsequently considered in the design. This paper summarizes a field study that consisted of NDE of six, full-scale drilled shafts with preinstalled voids and lateral-load tests that were performed on the six test shafts. Results from the field study indicated that undetectable (by NDE) void flaws occupying areas of up to 15% of the cross-sectional area of the drilled shaft could reduce free-head shear capacity up to 16%. A subsequent numerical analysis was performed to filter out all variables, other than void flaws, that could affect the lateral-load deformation of drilled shafts. Numerical analysis results validated the field tests measurements. A parametric study of variables affecting the load-deformation behavior of drilled shafts suggests that a reduction in moment capacity of up to 27% is possible with undetected voids present in the shafts that were tested.