Lateral Loading For Drilled Shafts

The lateral loads that are exerted on drilled shafts for highway structures are derived from earth pressures, centrifugal forces from moving vehicles, braking forces, wind loads, current forces from flowing water, wave forces in some unusual instances, ice loads, vessel impact and earthquakes, which are viewed as “extreme events” with a probability of occurrence that exceeds the design life of the bridge.

Brief Description of the P-Y Method

The “p-y Method” represents a relatively sophisticated model which can effectively capture the nonlinear aspects of the problem, and is the recommended method for design of drilled shafts for lateral loading. This approach is readily implemented using one of several available computer software packages.

The p-y method is a general method for analyzing laterally loaded piles and drilled shafts with combined axial and lateral loads, including distributed loads along the pile or shaft caused by flowing water or creeping soil, nonlinear bending characteristics, including cracked sections, layered soils and/or rock and nonlinear soil response.

The application of lateral load to a drilled shaft must result in some lateral deflection. This deflection   causes a soil reaction that acts in a direction opposite to the deflection; i.e., the soil pushes back. The magnitude of the soil reaction along the length of the drilled shaft is a nonlinear function of the deflection, and the deflection is dependent on the soil reaction.  The “p-y” method is so named because the soil resistance is modeled as a nonlinear spring in which the force due to soil resistance, p, develops as a function of deflection, y, and the relations between the two are modeled as p-y curves.

A physical model for the laterally-loaded drilled shaft is shown in Figure 3. A drilled shaft is shown in the figure with loading at the top. The soil has been replaced with a series of mechanisms that show the soil response in concept. At each depth, x, the soil reaction, p (resisting force per unit length along the drilled shaft), is a nonlinear function of lateral deflection, y, and is defined by a curve that reflects the shear strength of the soil, its Young’s modulus, the position of the piezometric surface, the drilled shaft diameter, depth and whether the loading is static (monotonic) or cyclic.

The computational procedure is dependent on being able to represent the response of the soil by an appropriate family of p-y curves. Full-scale experiments and theory have been used and recommendations have been presented for obtaining p-y curves, both for static and for cyclic loading.  . These models have been programmed as subroutines to computer programs, and the user merely needs to input the loadings, the section geometry of the drilled shaft and its stiffness, and the soil, steel and concrete properties. Other p-y methods can also be specified (e.g., Murchison and O’Neill, 1984, the API method for sands; Reese, 1997, an updated method for rock based on analysis of loading tests), and additional relations will likely be added as research and field experiments allow for their development.  Site-specific p-y relationships as obtained from field loading tests can also be input by the user. 

Simulation of Nonlinear Bending in Drilled Shafts 

For design of drilled shafts under lateral loading, the engineer must recognize that the shaft is essentially a reinforced concrete beam-column and that its bending behavior cannot always be appropriately represented by a simple linear elastic beam, that is, by a single EI value. If the purpose of the analysis is to determine moments and shears within the shaft in order to design the reinforcing steel and to obtain the appropriate diameter, a linear analysis will almost always be sufficient. But, if the purpose of the analysis is to estimate deflections and rotations of the head of the shaft, nonlinear bending should be considered.

Software used to compute moments, shears and deformations in the drilled shaft using the p-y method  contain subroutines that automatically perform these computations The user need only input the strength properties of the concrete and steel and the geometric properties of the cross section and longitudinal rebar. The deflected shape, shears and moments that are computed for the drilled shaft with a prescribed system of loads then reflect the effects of nonlinear bending, including cracking.

Guidelines for Selection of Appropriate P-Y Criteria for Design

The P-Y criteria are simply a means of associating the soil resistance mobilized as a nonlinear function of displacement at various points along a drilled shaft.  Although there may exist a theoretical basis in many cases, the criteria used in design are empirical in that the final form of the models used are derived from experiments (instrumented load tests).  Therefore, it is necessary that the user understand the experimental basis for a P-Y criterion that is being used so that limitations are understood and for the models to be used for appropriate conditions.

Cohesive Soils

Several criteria are available for modeling cohesive soils, and the most commonly used include those for  soft clays (Matlock, 1970), stiff clays (Welch and Reese, 1972) and stiff clays in the presence of free water (Reese et al., 1975).  Each of these are characterized by the use of a polynomial to model the nonlinear relationship of soil resistance versus displacement followed by an upper bound,The input soil parameter that most significantly affects the response of a drilled shaft in cohesive soils using p-y curves for these criteria is the soil cohesion (undrained shear strength, S_u), which directly affects the ultimate soil resistance, P_u.  The undrained shear strength used to develop the p-y criteria is typically measured using unconsolidated, undrained (UU) triaxial compression tests with confining pressures at or near the total overburden pressure.

A parameter which has a somewhat less significant effect in cohesive soils is the initial stiffness, Esi.  Esi is most commonly related to a stiffness parameter, ε50, which is intended to represent the strain at an axial compressive stress equal to 50% of the yield stress in the UU triaxial test.  Typical values of ε50 are often simply associated with a given range of S_u.

The use of undrained shear strength, Su, has proven to provide a reliable correlation with load test results of short duration.  The instrumented field loading tests performed to develop these criteria have typically been performed within a period of a few hours, so this model of soil resistance is appropriate for short duration loadings typical of live loads on highway structures.  Long duration sustained loads may actually mobilize a softer response due to creep, and extremely short duration transient loads may actually mobilize a stiffer response due to rate of loading effects.

Engineers using these p-y criteria to design a drilled shaft for lateral loading should perform analyses using a range of values of S_u and ε50 to evaluate the sensitivity of the analysis to these parameters.  There always exists uncertainty in the evaluation of in-situ soil properties as well as in the relationship of these properties to the ultimate performance of the foundation.  Sensitivity studies can provide the information needed to develop judgment regarding the reliability of the design and the relative importance of various input parameters.

Cohesionless Soils (Sands)

Several criteria are available for modeling cohesionless soils, and the most commonly used include Cox,  et al. (1974) and the very similar criterion of Murchison and O’Neill (1984) that has been adopted as a standard by the American Petroleum Institute.  Each of these are characterized by an initial linear stiffness followed by a polynomial to model the transition to an upper bound, as shown in following figure.

The input soil parameter that most significantly affects the response of a drilled shaft in sand using p-y curves for these criteria is the modulus value, k, which directly affects the initial straight line portion of the curve.  The values used for this parameter k are estimated within the range of 20 to 225 lb/in. 3  based  on an assessment of the relative density of the sand and the effect of a submerged or dry condition.  The ultimate resistance, Pu, is related to the angle of internal friction (φ) and the confining pressure, but the lateral response of drilled shafts in sand is less sensitive to φ than to k.

Correlations with In-Situ Tests

There exist a number of published correlations for computing p-y curves based upon the results of in-situ tests such as the pressuremeter (Briaud, 1992) or dilatometer (Robertson et al., 1985). In general, these test data rely on empirical correlations with test measurements to develop p-y curves for design, with consideration of soil type, depth, and shaft diameter.  Comparative evaluations suggest that these tools can provide useful correlations (Anderson et al., 2003); as with any empirical relationship, calibration to field load tests in geologic conditions which are representative of the local area provide the most reliable application of these correlations for design.

Limitations  P_Y approach

A significant limitation of the p-y approach is that it is mostly empirical ,In addition, p-y methods are generally more applicable to deep foundations that are relatively long and slender, and as a result, can bend and deflect, i.e., structural failure of the deep foundation element in bending usually controls. The p-y methodology is not fully applicable to short piles/shafts that tend to rotate, where soil failure near the ground surface controls.  Also, care must be used for large diameter elements, such as large diameter drilled shafts, because the majority of published curves were developed based on smaller diameter elements.

Alternative Models for Computation of Shaft Response

Although the p-y method is recommended for design, available alternative models can be employed in some circumstances.  The Broms Method (Broms, 1964a, 1964b, and 1965), offers a simple computation method that may be useful for sign or sound wall foundations constructed using short drilled shafts.  In addition, the Broms Method provides a rational limit equilibrium solution which is easy to understand in terms of the basic principles of computing the strength limits of a simple problem.  Several other alternative models include those based on elastic continuum, boundary element, and finite element models.  An overview of these models is included in GEC-9 (Parkes, et al., 2018)

Determine the spring stiffness

The process to determine the spring stiffness and structure response to analyze the drilled shafts using the p-y approach is iterative.  It normally requires two computational tools: (1) a soil-structure interaction analysis to generate the p-y curves  and evaluate the soil stiffness, such as LPILE    or  COM624P  and, (2) a structural analysis to evaluate the structural responses, such as SAP2000 & CSI BRIDGE  

The iterative procedure for establishing factored force effects on the drilled shafts can be summarized as follows:

1.The structural model(SAP2000 ) is analyzed under the factored loads;  load combinations and load factors; drilled shaft lateral spring constants initially are assumed,

2.Force effects calculated by the structural modeling program from Step 1 the head of the shaft are resolved into axial, lateral, and moment components

3.The factored axial, lateral, and moment force effects from Step 2 are used as the applied loads for analyzing trial drilled shafts by the p-y method of analysis(LPILE or COM624P);  p-y curves are established on the basis of soil properties and the idealized subsurface profile;

4.Results of the p-y analysis are used to evaluate lateral stiffness versus lateral deflection along the length of the drilled shaft;  these stiffness profiles are used to develop revised spring constants in subsequent structural modeling

5.The structural model is re-analyzed using the revised lateral spring constants established in Step 4; drilled shafts are modeled as beam-column elements;

6. Steps 3, 4, and 5 are repeated iteratively until lateral deflections calculated by the structural modeling program and p-y analyses show agreement to within + 20 percent

Figure 6 illustrates the procedure for determining the spring stiffness.