The worldwide state of practice for simulating static and seismic soil-pile interaction is to use a set of one-dimensional springs along pile shafts. This approach is also referred to as Beam on Nonlinear Winkler Foundation (BNWF). Due to its simplicity, the method is widely used in almost all engineering firms around the world for the design of pile either in a small-scale projects like parking structures or in large-scale projects like cable-stayed bridge systems.

Note that in this method  three-dimensional configuration of soil continuum which is highly anisotropic and nonlinear elast0pastic is simulated by uncoupled one-dimensional springs. One my ask two extremely important question:

Q#1: Considering the above-mentioned fact about spring method, can we really rely on this method and can we base our design on its outputs?

As part of my PhD studies I evaluated the validity of this approach. I used the BNWF approach to simulate twenty-seven static field tests and two dynamic centrifuge tests. You can read Chapter 6 of my dissertation (Click here) for further details and outcomes of the study. I found out that the error in estimation of pile response can be very significant (on the order of ±150%). The reasons for such considerable amount of error are listed below:

• Soil-pile interaction is highly nonlinear and hysteretic. Simulating this complex response by a simple one-dimensional spring will be surely associated with significant level of error.
• Continuous three-dimensional configuration of soil domain cannot be simulated by uncoupled one-dimensional springs. Soil-pile interaction in direction X would affect the interaction in other directions.
• In dynamic/seismic soil-pile interaction, the soil mass that is affected by the kinematic and inertial interactions is not included in the numerical model. So it is not a big surprise to notice a significant difference in modal responses.
• In seismic soil-pile interaction, since seismic motions are calculated in the free-field in an uncoupled manner without accounting for the effects of inertial and kinematic interaction of soil and pile, the seismic response of the system will be different that reality.

I noted that BNWF approach can satisfactorily simulate a pile response if:

1. Loading condition is static, and
2. Site-specific p-y, t-z, and Q-z curves are obtained by performing a fully instrumented load test at the project site.

This confirms some engineers’ claims that the BNWF approach is reliable based on their past project experience where they used the approach for analysis of a test pile and the model satisfactorily predicted the pile test results. If you input an appropriate set of springs at soil-pile interface, you would be able to satisfactorily predict pile performance. However, if you don’t have site-specific springs, there is a high probability that you misestimate pile response. Based on my evaluation, for seismic loading condition, even if you use site-specific springs you will not be able to appropriately estimate pile seismic response.

Q#2: If spring method is not reliable, what method should be used alternatively?

I dedicated one year of my PhD studies to finding an answer to this question. I tried adding some additional component to the spring model such as strain-hardening component, dashpot, etc. But I could still  find several other cases that the outputs of spring method were off. On the other hand, fully coupled continuum models of pile and foundation soil were capable of  capturing pile responses. I encountered one or two cases that results of continuum model were slightly off and that was because I had a little information about the insitu soil properties.

In my opinion, with the aid of new advances in computational tools where computer analyses can be executed much faster, engineers should move to the next level of design by numerical modeling. Spring methods were proposed several decades ago where computers either did not exist or were not commonly used in engineering offices. Based on my findings both in academia and industry, a continuum model in which soil behavior is simulated by a very simple constitutive model (elastic-perfectly plastic models) is way more reliable than a spring model.