Page 26 - Analysis and Design of Energy Geostructures

List of symbols xxvii

Roman symbols
Symbol Variable name Unit measure
Vertical head displacement of the receiver pile in a pair m
w i
Vertical head displacement of a single isolated pile m
w j
Vertical displacement of a single source pile in a group m
w
1 Unitary vertical displacement m
w
Unitary vertical displacement caused by a mechanical load m
1;m
w
Unitary vertical displacement caused by a thermal load m
1;th
w
th Vertical displacement under free thermal expansion conditions m
w
f
w q b =2 Vertical base displacement mobilised for q b =2 m
w q s =2 Vertical shaft displacement mobilised for q s =2 m
Crack width m
w k
Water content %
w n
Weight of the considered body N
W;W i
Weight of solid N
W s
Weight of water N
W w
Shear distribution m
W 1
Coordinate (e.g., horizontal) m
x
Material parameter
x H
Pipe length m
x p
Normalised distance
~ x
Integral variable with the dimension of time m
x t
Thermal entry length m
x fd;th
Hydrodynamic entry length m
x fd;h
Haigh equation parameter
x H
Material or product design properties
X d;i
Material or product characteristic properties
X k;i
Soil pile thermal expansion coefficient ratio
X
3
X Body forces in the x direction N/m
Component of the prescribed stress vector in the x direction Pa
X
Horizontal coordinate m
y
Y B;0 Second kind Bessel function of first order
Y B;1 Second kind Bessel function of second order

Second kind Bessel function of order n
Y B;n
Body forces in the y direction N/m 3
Y
Component of prescribed stress vector in the y direction Pa
Y
Vertical coordinate or depth m
z
Shape function
z G
Empirical constant
z M
Distance of thermocouples m
z tc
Minimum depth m
z min
Maximum depth m
z max
Specific vertical coordinate; inner level arm m
~ z
Depth of null point of vertical displacement m
z NP;w
z NP;τ Depth of null point of shear stress m
Body forces in the z direction N/m 3
Z
Component of prescribed stress vector in the z direction Pa
Z