Interaction Model for Torsional Dynamic Response of Thin-Wall Pipe Piles Embedded in Both Vertically and Radially Inhomogeneous Soil

Acknowledgments

Notation

$c_{s,k}^{}$

material damping coefficient of the k-th inner soil (soil plug) sphere of the s-th pile segment;

$G_s^p$

shear modules of the s-th pipe pile segment;

$G_{s,j}^{s1}$

shear modules of the j-th surrounding soil sphere of the s-th pile segment;

H

length of the pipe pile;

h_s

buried depth of the upper surface of the s-th pile segment;

$I_s^p$

polar moment of inertia of the s-th pipe pile segment;

$I_{s,k}^{s2}$

polar moment of inertia of the k-th inner soil (soil plug) sphere of the s-th pile segment;

k_s,k

elastic modules of the k-th inner soil (soil plug) sphere of the s-th pile segment;

l_s

length of the s-th pile segment;

r₁

outer radii of the pipe pile;

r₂

inner radii of the pipe pile;

r_s,k

outer radius of the k-th sphere of the s-th soil–pile segment;

t

number of spheres divided in the inner soil;

t_m

disturbed range of inner soil (soil plug) and surrounding soil;

y

number of spheres divided in the surrounding soil;

${\eta }_s^p$

material damping coefficient of the s-th pipe pile segment;

${\eta }_{s,j}^{s1}$

material damping coefficient of the j-th surrounding soil sphere of the s-th pile segment;

${\rho }_s^p$

density of the s-th pipe pile segment;

${\rho }_{s,j}^{s1}$

density of the j-th surrounding soil sphere of the s-th pile segment;

${\rho }_{s,k}^{s2}$

density of the k-th inner soil (soil plug) sphere of the s-th pile segment;

${\phi }_s^p$

twist angle of the s-th pipe pile segment;

${\phi }_{s,j}^{s1}$

twist angle in the j-th surrounding soil sphere of the s-th pile segment; and

${\phi }_{s,j}^{s2}$

twist angle in the j-th inner soil (soil plug) sphere of the s-th pile segment.

References