Abstract:
In civil engineering, pile foundations are essential elements in structural design in soft
soils. The fact that piles are driven deep into the ground thus to interact mostly with
saturated soil layers, their interaction with surrounding soils remain one of the most
urgently important parts of the whole structure. In this paper, the integral equation method
is employed to develop a model that predicts the time-dependent behavior of an axially
loaded pile embedded in a layered transversely isotropic saturated soil (TISS). Based on
the fictitious pile method, the pile-soil system is decomposed into an extended saturated
half-space and a fictitious pile. The extended half-space is treated as a layered TISS, while
the fictitious pile is considered as a 1D bar. The fundamental solution of the layered TISS
is gotten by the means of the RTM method for the layered TISS. The detailed contents of
this paper consist of the following parts:
1. First, the RTM method is used to produce the elementary solutions, which
corresponds to the time-dependent response of the layered TISS to a uniformly-
distributed load acting vertically over a circular area with the radius equal to that of
the pile. A system of partial differential equations is derived based on the governing
equations of Biot’s consolidation of TISS in cylindrical coordinate system. Then,
employing the Hankel transforms and the Laplace transforms with respect to the
radial coordinate r and the time t, respectively, a system of ordinary differential
equations is derived in the transformed domain. Solving the differential equations
will result in the general solution and the transform matrix relating the state vector and the static wave vector is introduced. Later, the solution in the transformed
domain to the layered TISS subjected to an external vertical force is deduced from
the reflection and transmission matrices (RTMs) developed based on the wave
vector transform matrix. The time domain solution to the layered TISS subjected to
an external vertical force is retrieved with the use of the inverse Hankel-Laplace
transform.
2. By using the fundamental solution developed for a layered TISS together with
adopting the fictitious pile method due to Muki & Sternberg, the behavior of piles
embedded in layered TISS is also studied in this paper. The pile-soil compatibility
is accomplished by requiring that the axial strain of the fictitious pile be equal to
the vertical strain of the extended layered TISS along the axis of the pile. The
second kind Fredholm integral equation of the pile is then derived by using the
aforementioned compatibility condition and the fundamental solution of the layered
TISS. Applying the Laplace transform to the Fredholm integral equation, and
solving the resulting integral equation, the transformed solution is obtained. Then
the approximate time domain Fredholm integral equation of the second kind is
obtained by the Schapery method.
3. Finally, employing the Fortran software, numerical results are obtained and
discussed. First, an example is presented to discuss the impact of different soil
parameters on the response of the layered TISS. Then, results obtained by the
proposed integral equations for the pile agree with existing solutions very well,
validating the proposed pile-soil interaction model. Later, using different parametric examples, a parametric study is performed to examine the influence of
some parameters of the pile-soil system on its response.