ssi.py
SSI functions.
nist2012soil important notes:
2.3: Rotational (or cross rotational-translational) impedance of single piles is omitted because rotational stiffness is typically derived from groups of piles supporting a footing or mat, which is based on vertical response parameters.
An important consideration when piles are combined with shallow spread footings or a mat foundation is whether or not lateral resistance is provided by the shallow foundation elements in combination with the piles. Soil might be expected to settle away from shallow foundation elements in cases involving clayey foundation soils and end-bearing piles, particularly when there are surface fills at the site. In such cases, lateral load resistance would derive solely from the piles and basement walls.
8.2.1: An important consideration when deep foundation elements (e.g., piles) are combined with shallow foundation elements (e.g., spread footings or mats) is whether or not resistance from both shallow and deep foundation elements can be combined. If the soil is expected to settle away from the shallow foundation elements (e.g., the case of consolidating soils and end-bearing piles), then lateral load resistance should be derived on the basis of the piles, pile caps, and basement walls only, and the resistance provided by shallow foundation elements should be ignored.
Classes:
| Name | Description |
|---|---|
ReferenceFigureRegistry |
Pre-instantiated reference figures |
Functions:
Pre-instantiated reference figures
get_active_pile_length(
elasticity_modulus,
pile_elasticity_modulus,
pile_diameter,
is_homogeneous_soil=True,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_active\_pile\_length}(E_s, E_p, D, \mathrm{is\_homogeneous\_soil}) \\ \hspace{1em} \mathbf{if} \ \mathrm{is\_homogeneous\_soil} \\ \hspace{2em} \mathopen{}\left( χ, n \mathclose{}\right) \gets \mathopen{}\left( 2.4, 0.25 \mathclose{}\right) \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathopen{}\left( χ, n \mathclose{}\right) \gets \mathopen{}\left( 2.5, 0.2 \mathclose{}\right) \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} L_a \gets χ \cdot \mathopen{}\left( \frac{E_p}{E_s} \mathclose{}\right)^{n} D \\ \hspace{1em} \mathbf{return} \ L_a \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
elasticity_modulus
|
float
|
Modulus of elasticity of soil |
required |
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
is_homogeneous_soil
|
bool
|
Indicates if soil is homogeneous |
True
|
Returns:
| Name | Type | Description |
|---|---|---|
active_pile_length |
float
|
Active pile length in lateral mode (typically < L_p) |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_average\_bottom\_depth}(D_f, z_p) \\ \hspace{1em} z_{bottom} \gets D_f + z_p \\ \hspace{1em} \mathbf{return} \ z_{bottom} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
footing_embedment
|
float
|
Depth of footing embedment |
required |
effective_profile_depth
|
float
|
Effective profile depth for analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
average_bottom_depth |
float
|
Special average bottom depth |
get_average_effective_shear_velocity(
shear_velocity,
depth,
average_top_depth,
average_bottom_depth,
shear_modulus_reduction_factor,
unit_weight,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_average\_effective\_shear\_velocity}(V_s, z, z_{top}, z_{bottom}, G/G_0, γ) \\ \hspace{1em} V_{s,avg} \gets \mathrm{\_get\_average\_effective\_shear\_velocity} \mathopen{}\left( V_s, z, z_{top}, z_{bottom} \mathclose{}\right) \\ \hspace{1em} V_{s,avg\ red} \gets V_{s,avg} \cdot \sqrt{ G/G_0 } \\ \hspace{1em} G \gets \mathrm{get\_small\_strain\_shear\_modulus\_\_landau1959theory} \mathopen{}\left( γ, V_{s,avg\ red} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ \mathopen{}\left( V_{s,avg}, V_{s,avg\ red}, G \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
shear_velocity
|
float
|
Shear wave velocity of soil |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
average_top_depth
|
float
|
Special average top depth |
required |
average_bottom_depth
|
float
|
Special average bottom depth |
required |
shear_modulus_reduction_factor
|
float
|
Shear modulus reduction factor for soil |
required |
unit_weight
|
float
|
Unit weight of soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
average_effective_shear_velocity |
float
|
Average effective profile velocity |
average_effective_shear_velocity_reduced |
float
|
Average effective profile velocity reduced for strain compatibility |
shear_modulus |
float
|
Shear modulus of soil |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_average\_effective\_shear\_velocity\_xx}(V_s, z, z_p) \\ \hspace{1em} \mathrm{average\_effective\_shear\_velocity\_xx} \gets \mathrm{get\_site\_class\_average} \mathopen{}\left( V_s, z \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ \mathrm{average\_effective\_shear\_velocity\_xx} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
shear_velocity
|
float
|
Shear wave velocity of soil |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
effective_profile_depth_rotation
|
float
|
Effective profile depth for foundation rotation |
required |
Returns:
| Name | Type | Description |
|---|---|---|
average_effective_shear_velocity |
float
|
Average effective profile velocity |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_average\_top\_depth}(\mathrm{foundation\_is\_embedded}, D_f) \\ \hspace{1em} z_{top} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathrm{foundation\_is\_embedded}, D_f, 0 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ z_{top} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
foundation_is_embedded
|
bool
|
Indicates if foundation is embedded |
required |
footing_embedment
|
float
|
Depth of footing embedment |
required |
Returns:
| Name | Type | Description |
|---|---|---|
average_top_depth |
float
|
Special average top depth |
get_dashpot_coefficient(
stiffness,
radiation_damping_ratio,
soil_damping_ratio,
natural_frequency,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dashpot\_coefficient}(k, β, β_s, ω) \\ \hspace{1em} c \gets 2 k \frac{β + β_s}{ω} \\ \hspace{1em} \mathbf{return} \ c \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
stiffness
|
float
|
Dynamic stiffness for mode j (translation or rotation) |
required |
radiation_damping_ratio
|
float
|
Radiation damping ratio for soil |
required |
soil_damping_ratio
|
float
|
Hysteretic damping ratio of soil |
required |
natural_frequency
|
float
|
Undamped natural vibration frequency |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dashpot_coefficient |
float
|
Dashpot coefficient for translation (MN-s/m) or rotation (MN-m/rad) |
get_dashpot_coefficient_intensity(
dashpot_coefficient_intensity_vertical,
stiffness_edge_factor,
dashpot_edge_factor,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dashpot\_coefficient\_intensity}(c_z^i, R_k, R_c) \\ \hspace{1em} ci \gets c_z^i \cdot R_k \cdot R_c \\ \hspace{1em} \mathbf{return} \ ci \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dashpot_coefficient_intensity_vertical
|
float
|
Vertical dashpot coefficient intensity |
required |
stiffness_edge_factor
|
float
|
Stiffness edge increase factor |
required |
dashpot_edge_factor
|
float
|
Dashpot edge decrease factor |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dashpot_coefficient_intensity |
float
|
Dashpot coefficient intensity |
get_dashpot_coefficient_intensity_vertical(
vibration_mode,
dashpot_coefficient,
footing_half_width,
footing_half_length,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dashpot\_coefficient\_intensity\_vertical}(j, c, B_h, L_h) \\ \hspace{1em} \mathrm{dashpot\_coefficient\_map} \gets \mathrm{dict} \mathopen{}\left( \mathrm{zip} \mathopen{}\left( \mathrm{np}.\mathrm{atleast\_1d} \mathopen{}\left( j \mathclose{}\right), \mathrm{np}.\mathrm{atleast\_1d} \mathopen{}\left( c \mathclose{}\right) \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} c_z \gets \mathrm{dashpot\_coefficient\_map}_{\textrm{"z"}} \\ \hspace{1em} c_z^i \gets \frac{c_z}{4 B_h \cdot L_h} \\ \hspace{1em} \mathbf{return} \ c_z^i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
dashpot_coefficient
|
float
|
Dashpot coefficient for translation (MN-s/m) or rotation (MN-m/rad) |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dashpot_coefficient_intensity_vertical |
float
|
Vertical dashpot coefficient intensity |
get_dashpot_edge_factor(
end_length_ratio,
dashpot_coefficient,
stiffness_edge_factor,
dashpot_coefficient_intensity_vertical,
footing_half_width,
footing_half_length,
vibration_mode,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dashpot\_edge\_factor}(R_e, c, R_k, c_z^i, B_h, L_h, j) \\ \hspace{1em} \mathrm{condition\_1} \gets j = \textrm{"xx"} \\ \hspace{1em} \mathrm{choice\_1} \gets \frac{\frac{3 c}{4 c_z^i \cdot B_h^{3} \cdot L_h}}{R_k \cdot \mathopen{}\left( 1 - \mathopen{}\left( 1 - R_e \mathclose{}\right)^{3} \mathclose{}\right) + \mathopen{}\left( 1 - R_e \mathclose{}\right)^{3}} \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_2} \gets \frac{\frac{3 c}{4 c_z^i \cdot B_h \cdot L_h^{3}}}{R_k \cdot \mathopen{}\left( 1 - \mathopen{}\left( 1 - R_e \mathclose{}\right)^{3} \mathclose{}\right) + \mathopen{}\left( 1 - R_e \mathclose{}\right)^{3}} \\ \hspace{1em} \mathrm{condition\_3} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_3} \gets 1 \\ \hspace{1em} R_c \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ R_c \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
end_length_ratio
|
float
|
End length ratio |
required |
dashpot_coefficient
|
float
|
Dashpot coefficient for translation (MN-s/m) or rotation (MN-m/rad) |
required |
stiffness_edge_factor
|
float
|
Stiffness edge increase factor |
required |
dashpot_coefficient_intensity_vertical
|
float
|
Vertical dashpot coefficient intensity |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dashpot_edge_factor |
float
|
Dashpot edge decrease factor |
get_dimensionless_frequency(
natural_frequency,
footing_half_width,
average_effective_shear_velocity_reduced,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dimensionless\_frequency}(ω, B_h, V_{s,avg\ red}) \\ \hspace{1em} a_0 \gets \frac{ω \cdot B_h}{V_{s,avg\ red}} \\ \hspace{1em} \mathbf{return} \ a_0 \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
natural_frequency
|
float
|
Undamped natural vibration frequency |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
average_effective_shear_velocity_reduced
|
float
|
Average effective profile velocity reduced for strain compatibility |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dimensionless_frequency |
float
|
Dimensionless frequency for dynamic analysis |
get_dimensionless_frequency_pile(
natural_frequency,
pile_diameter,
average_effective_shear_velocity_reduced,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dimensionless\_frequency\_pile}(ω, D, V_{s,avg\ red}) \\ \hspace{1em} a_0 \gets \frac{ω \cdot D}{V_{s,avg\ red}} \\ \hspace{1em} \mathbf{return} \ a_0 \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
natural_frequency
|
float
|
Undamped natural vibration frequency |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
average_effective_shear_velocity_reduced
|
float
|
Average effective profile velocity reduced for strain compatibility |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dimensionless_frequency |
float
|
Dimensionless frequency for dynamic analysis |
get_dimensionless_pile_length_parameter(
pile_elasticity_modulus,
elasticity_modulus,
dimensionless_subgrade_reaction_modulus,
pile_diameter,
pile_embedment_length,
vibration_mode,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dimensionless\_pile\_length\_parameter}(E_p, E_s, δ, D, L, j) \\ \hspace{1em} \mathrm{condition\_1} \gets \mathopen{}\left( j = \textrm{"z"} \mathclose{}\right) \mathbin{\&} \mathopen{}\left( D \ne 0 \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_1} \gets \mathopen{}\left( \frac{4 δ}{\mathrm{np}.\pi} \mathclose{}\right)^{\frac{1}{2}} \mathopen{}\left( \frac{E_p}{E_s} \mathclose{}\right)^{\frac{-1}{2}} \frac{L}{D} \\ \hspace{1em} λL \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ λL \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
elasticity_modulus
|
float
|
Modulus of elasticity of soil |
required |
dimensionless_subgrade_reaction_modulus
|
float
|
Dimensionless modulus of subgrade reaction |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
pile_embedment_length
|
float
|
Embedment length of pile |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dimensionless_pile_length_parameter |
float
|
Dimensionless pile length parameter |
get_dimensionless_pile_length_parameter_ksd(
pile_elasticity_modulus,
pile_moment_of_inertia,
vibration_mode,
subgrade_reaction_modulus_at_diameter,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dimensionless\_pile\_length\_parameter\_ksd}(E_p, I_p, j, k_{sd}) \\ \hspace{1em} \mathrm{condition\_1} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_1} \gets \mathopen{}\left( \frac{k_{sd}}{4 E_p \cdot I_p} \mathclose{}\right)^{\frac{1}{4}} \\ \hspace{1em} λL \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ λL \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
pile_moment_of_inertia
|
float
|
Moment of inertia of equivalent solid pile |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
subgrade_reaction_modulus_at_diameter
|
float
|
Subgrade reaction modulus at one pile diameter |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dimensionless_pile_length_parameter |
float
|
Dimensionless pile length parameter |
get_dimensionless_pile_tip_stiffness(
pile_elasticity_modulus,
elasticity_modulus,
dimensionless_subgrade_reaction_modulus,
poisson_ratio,
vibration_mode,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dimensionless\_pile\_tip\_stiffness}(E_p, E_s, δ, ν, j) \\ \hspace{1em} \mathrm{condition\_1} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_1} \gets \frac{2}{\sqrt{ \mathrm{np}.\pi \cdot δ } \cdot \mathopen{}\left( 1 - ν^{2} \mathclose{}\right)} \mathopen{}\left( \frac{E_p}{E_s} \mathclose{}\right)^{\frac{-1}{2}} \\ \hspace{1em} Ω \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ Ω \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
elasticity_modulus
|
float
|
Modulus of elasticity of soil |
required |
dimensionless_subgrade_reaction_modulus
|
float
|
Dimensionless modulus of subgrade reaction |
required |
poisson_ratio
|
float
|
Poisson’s ratio of soil |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dimensionless_pile_tip_stiffness |
float
|
Dimensionless pile tip stiffness |
get_dimensionless_subgrade_reaction_modulus(
pile_elasticity_modulus,
elasticity_modulus,
vibration_mode,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dimensionless\_subgrade\_reaction\_modulus}(E_p, E_s, j) \\ \hspace{1em} \mathrm{condition\_1} \gets \mathrm{np}.\mathrm{isin} \mathopen{}\left( j, \mathopen{}\left( \textrm{"x"}, \textrm{"y"} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_1} \gets 2 \mathopen{}\left( \frac{E_p}{E_s} \mathclose{}\right)^{\frac{-3}{40}} \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_2} \gets 0.6 \\ \hspace{1em} \mathrm{condition\_3} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_3} \gets 1.2 \\ \hspace{1em} δ \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ δ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
elasticity_modulus
|
float
|
Modulus of elasticity of soil |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dimensionless_subgrade_reaction_modulus |
float
|
Dimensionless modulus of subgrade reaction |
get_displacement_rotation(
pile_swaying_stiffness,
pile_rocking_stiffness,
pile_cross_swaying_rocking_stiffness,
pile_head_lateral_load,
pile_head_moment,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_displacement\_rotation}(K_{hh}, K_{rr}, K_{hr}, \mathrm{pile\_head\_lateral\_load}, \mathrm{pile\_head\_moment}) \\ \hspace{1em} \mathrm{stiffness\_matrix\_inverted} \gets \frac{1}{K_{hh} \cdot K_{rr} - K_{hr}^{2}} \cdot \mathrm{np}.\mathrm{asarray} \mathopen{}\left( \mathopen{}\left[ \mathopen{}\left[ K_{rr}, -K_{hr} \mathclose{}\right], \mathopen{}\left[ -K_{hr}, K_{hh} \mathclose{}\right] \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathopen{}\left( u, θ \mathclose{}\right) \gets \mathrm{np}.\mathrm{matmul} \mathopen{}\left( \mathrm{stiffness\_matrix\_inverted}, \mathrm{np}.\mathrm{asarray} \mathopen{}\left( \mathopen{}\left[ \mathrm{pile\_head\_lateral\_load}, \mathrm{pile\_head\_moment} \mathclose{}\right] \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ \mathopen{}\left( u, θ \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_swaying_stiffness
|
float
|
Swaying stiffness of pile |
required |
pile_rocking_stiffness
|
float
|
Rocking stiffness of pile |
required |
pile_cross_swaying_rocking_stiffness
|
float
|
Cross-swaying-rocking stiffness of pile |
required |
pile_head_lateral_load
|
float
|
Lateral load at pile head |
required |
pile_head_moment
|
float
|
Moment at pile head |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_head_displacement |
float
|
Displacement at pile head |
pile_head_rotation |
float
|
Rotation at pile head |
get_dynamic_stiffness_modifier(
dimensionless_frequency,
footing_half_length,
footing_half_width,
vibration_mode,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dynamic\_stiffness\_modifier}(a_0, L_h, B_h, j) \\ \hspace{1em} \mathrm{condition\_1} \gets \mathrm{np}.\mathrm{isin} \mathopen{}\left( j, \mathopen{}\left( \textrm{"x"}, \textrm{"y"} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_1} \gets 1 \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_2} \gets 1 - \frac{\mathopen{}\left( 0.4 + \frac{0.2}{\frac{L_h}{B_h}} \mathclose{}\right) a_0^{2}}{\frac{10}{1 + 3 \mathopen{}\left( \frac{L_h}{B_h} - 1 \mathclose{}\right)} + a_0^{2}} \\ \hspace{1em} \mathrm{condition\_3} \gets j = \textrm{"xx"} \\ \hspace{1em} \mathrm{choice\_3} \gets 1 - \frac{\mathopen{}\left( 0.55 + 0.01 \sqrt{ \frac{L_h}{B_h} - 1 } \mathclose{}\right) a_0^{2}}{2.4 - \frac{0.4}{\mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3}} + a_0^{2}} \\ \hspace{1em} \mathrm{condition\_4} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_4} \gets 1 - \frac{0.55 a_0^{2}}{0.6 + \frac{1.4}{\mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3}} + a_0^{2}} \\ \hspace{1em} \mathrm{condition\_5} \gets j = \textrm{"zz"} \\ \hspace{1em} \mathrm{choice\_5} \gets 1 - \frac{0.33 - 0.03 \sqrt{ \frac{L_h}{B_h} - 1 } \cdot a_0^{2}}{\frac{0.8}{1 + 0.33 \mathopen{}\left( \frac{L_h}{B_h} - 1 \mathclose{}\right)} + a_0^{2}} \\ \hspace{1em} α \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3}, \mathrm{condition\_4}, \mathrm{condition\_5} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3}, \mathrm{choice\_4}, \mathrm{choice\_5} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ α \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
dynamic_stiffness_modifier |
float
|
Frequency-dependent stiffness modifier for mode j |
get_dynamic_stiffness_modifier_pile(
dimensionless_subgrade_reaction_modulus,
pile_unit_weight,
unit_weight,
poisson_ratio,
dimensionless_frequency,
vibration_mode,
stiffness_weight_factor_soil=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_dynamic\_stiffness\_modifier\_pile}(δ, γ_p, γ, ν, a_0, j, w_s) \\ \hspace{1em} \mathrm{condition\_1} \gets j = \textrm{"x"} \\ \hspace{1em} \mathrm{choice\_1} \gets 1 - \frac{3 \mathrm{np}.\pi}{32 δ} \frac{\frac{γ_p}{γ}}{1 + ν} \cdot a_0^{2} \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_2} \gets 1 - w_s \cdot \mathopen{}\left( \frac{\mathrm{np}.\pi}{8 δ} \frac{\frac{γ_p}{γ}}{1 + ν} \cdot a_0^{2} - \frac{1}{2} \cdot a_0^{\frac{1}{2}} \mathclose{}\right) \\ \hspace{1em} α \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ α \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_subgrade_reaction_modulus
|
float
|
Dimensionless modulus of subgrade reaction |
required |
pile_unit_weight
|
float
|
Unit weight of pile material |
required |
unit_weight
|
float
|
Unit weight of soil |
required |
poisson_ratio
|
float
|
Poisson’s ratio of soil |
required |
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
stiffness_weight_factor_soil
|
float
|
Weight factor for soil stiffness contribution |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
dynamic_stiffness_modifier |
float
|
Frequency-dependent stiffness modifier for mode j |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_effective\_profile\_depth}(j, B_h, L_h) \\ \hspace{1em} \mathrm{condition\_1} \gets \mathrm{np}.\mathrm{isin} \mathopen{}\left( j, \mathopen{}\left( \textrm{"x"}, \textrm{"y"}, \textrm{"z"} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_1} \gets \mathopen{}\left( B_h \cdot L_h \mathclose{}\right)^{0.5} \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"xx"} \\ \hspace{1em} \mathrm{choice\_2} \gets \mathopen{}\left( B_h^{3} \cdot L_h \mathclose{}\right)^{0.25} \\ \hspace{1em} \mathrm{condition\_3} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_3} \gets \mathopen{}\left( B_h \cdot L_h^{3} \mathclose{}\right)^{0.25} \\ \hspace{1em} \mathrm{condition\_4} \gets j = \textrm{"zz"} \\ \hspace{1em} \mathrm{choice\_4} \gets \mathopen{}\left( B_h^{3} \cdot L_h + B_h \cdot L_h^{3} \mathclose{}\right)^{0.25} \\ \hspace{1em} z_p \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3}, \mathrm{condition\_4} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3}, \mathrm{choice\_4} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ z_p \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
effective_profile_depth |
float
|
Effective profile depth for analysis |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_effective\_profile\_depth\_pile}(j, L, L_a) \\ \hspace{1em} \mathrm{condition\_1} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_1} \gets L \\ \hspace{1em} \mathrm{condition\_2} \gets \mathrm{np}.\mathrm{isin} \mathopen{}\left( j, \mathopen{}\left( \textrm{"x"}, \textrm{"y"} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_2} \gets L_a \\ \hspace{1em} z_p \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ z_p \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
pile_embedment_length
|
float
|
Embedment length of pile |
required |
active_pile_length
|
float
|
Active pile length in lateral mode (typically < L_p) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
effective_profile_depth |
float
|
Effective profile depth for analysis |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_effective\_profile\_depth\_rotation}(D_f, B_h, L_h) \\ \hspace{1em} z_p \gets D_f + \mathrm{get\_effective\_profile\_depth} \mathopen{}\left( \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ z_p \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
footing_embedment
|
float
|
Depth of footing embedment |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
effective_profile_depth_rotation |
float
|
Effective profile depth for foundation rotation |
get_elasticity_modulus_z(
elasticity_modulus,
depth,
pile_diameter,
soil_profile_shape,
inhomogeneity_alpha=float("nan"),
inhomogeneity_exponent=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_elasticity\_modulus\_z}(E_s, z, D, \mathrm{soil\_profile\_shape}, a, n) \\ \hspace{1em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"linear"} \\ \hspace{2em} n \gets 1.0 \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathrm{elasticity\_modulus\_z} \gets E_s \cdot \mathopen{}\left( a + \frac{\mathopen{}\left( 1 - a \mathclose{}\right) z}{D} \mathclose{}\right)^{n} \\ \hspace{1em} \mathbf{return} \ \mathrm{elasticity\_modulus\_z} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
elasticity_modulus
|
float
|
Modulus of elasticity of soil |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
soil_profile_shape
|
str
|
Shape of soil profile |
required |
inhomogeneity_alpha
|
float
|
Inhomogeneity alpha parameter |
float('nan')
|
inhomogeneity_exponent
|
float
|
Inhomogeneity exponent for soil |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
elasticity_modulus |
float
|
Modulus of elasticity of soil |
get_embedment_factor(
footing_embedment,
footing_half_length,
footing_half_width,
vibration_mode,
foundation_is_embedded,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_embedment\_factor}(D_f, L_h, B_h, j, \mathrm{foundation\_is\_embedded}) \\ \hspace{1em} \mathrm{condition\_1} \gets \mathrm{foundation\_is\_embedded} \\ \hspace{1em} \mathrm{choice\_1} \gets \mathrm{float} \mathopen{}\left( \textrm{"nan"} \mathclose{}\right) \\ \hspace{1em} \mathrm{condition\_2} \gets \mathrm{np}.\mathrm{isin} \mathopen{}\left( j, \mathopen{}\left( \textrm{"x"}, \textrm{"y"} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_2} \gets 1 + \mathopen{}\left( 0.33 + \frac{1.34}{1 + \frac{L_h}{B_h}} \mathclose{}\right) \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{0.8} \\ \hspace{1em} \mathrm{condition\_3} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_3} \gets 1 + \mathopen{}\left( 0.25 + \frac{0.25}{\frac{L_h}{B_h}} \mathclose{}\right) \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{0.8} \\ \hspace{1em} \mathrm{condition\_4} \gets j = \textrm{"xx"} \\ \hspace{1em} \mathrm{choice\_4} \gets 1 + \frac{D_f}{B_h} + \frac{1.6}{0.35 + \frac{L_h}{B_h}} \cdot \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{2} \\ \hspace{1em} \mathrm{condition\_5} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_5} \gets 1 + \frac{D_f}{B_h} + \frac{1.6}{0.35 + \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{4}} \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{2} \\ \hspace{1em} \mathrm{condition\_6} \gets j = \textrm{"zz"} \\ \hspace{1em} \mathrm{choice\_6} \gets 1 + \mathopen{}\left( 1.3 + \frac{1.32}{\frac{L_h}{B_h}} \mathclose{}\right) \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{0.9} \\ \hspace{1em} η \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3}, \mathrm{condition\_4}, \mathrm{condition\_5}, \mathrm{condition\_6} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3}, \mathrm{choice\_4}, \mathrm{choice\_5}, \mathrm{choice\_6} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ η \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
footing_embedment
|
float
|
Depth of footing embedment |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
foundation_is_embedded
|
bool
|
Indicates if foundation is embedded |
required |
Returns:
| Name | Type | Description |
|---|---|---|
embedment_factor |
float
|
Embedment correction factor for rigid footing spring constants |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_footing\_half\_length}(L) \\ \hspace{1em} L_h \gets \frac{L}{2} \\ \hspace{1em} \mathbf{return} \ L_h \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
footing_length
|
float
|
Footing length (large plan dimension) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
footing_half_length |
float
|
Footing half-length (large plan dimension) |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_footing\_half\_width}(B) \\ \hspace{1em} B_h \gets \frac{B}{2} \\ \hspace{1em} \mathbf{return} \ B_h \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
footing_width
|
float
|
Footing width (small plan dimension) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
footing_half_width |
float
|
Footing half-width (small plan dimension) |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_footing\_router}() \\ \hspace{1em} j_{group} \gets \mathopen{}\left[ \textrm{"x overall"}, \textrm{"y overall"}, \textrm{"x base spring"}, \textrm{"y base spring"}, \textrm{"z"}, \textrm{"xx"}, \textrm{"yy"}, \textrm{"zz"} \mathclose{}\right] \\ \hspace{1em} j \gets \mathopen{}\left[ \textrm{"x"}, \textrm{"y"}, \textrm{"x"}, \textrm{"y"}, \textrm{"z"}, \textrm{"xx"}, \textrm{"yy"}, \textrm{"zz"} \mathclose{}\right] \\ \hspace{1em} \mathrm{foundation\_is\_embedded} \gets \mathopen{}\left[ \mathrm{False}, \mathrm{False}, \mathrm{True}, \mathrm{True}, \mathrm{False}, \mathrm{False}, \mathrm{False}, \mathrm{False} \mathclose{}\right] \\ \hspace{1em} \mathbf{return} \ \mathopen{}\left( j_{group}, j, \mathrm{foundation\_is\_embedded} \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Args:
Returns:
| Name | Type | Description |
|---|---|---|
vibration_mode_group |
str
|
Vibration mode group |
vibration_mode |
str
|
Vibration mode for dynamic analysis |
foundation_is_embedded |
bool
|
Indicates if foundation is embedded |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_footing\_zone}(j, k, c) \\ \hspace{1em} \mathrm{stiffness\_map} \gets \mathrm{dict} \mathopen{}\left( \mathrm{zip} \mathopen{}\left( \mathrm{np}.\mathrm{atleast\_1d} \mathopen{}\left( j \mathclose{}\right), \mathrm{np}.\mathrm{atleast\_1d} \mathopen{}\left( k \mathclose{}\right) \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathrm{dashpot\_coefficient\_map} \gets \mathrm{dict} \mathopen{}\left( \mathrm{zip} \mathopen{}\left( \mathrm{np}.\mathrm{atleast\_1d} \mathopen{}\left( j \mathclose{}\right), \mathrm{np}.\mathrm{atleast\_1d} \mathopen{}\left( c \mathclose{}\right) \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} j \gets \mathopen{}\left[ \textrm{"z"}, \textrm{"xx"}, \textrm{"yy"}, \textrm{"xx and yy"} \mathclose{}\right] \\ \hspace{1em} k \gets \mathopen{}\left[ \mathrm{stiffness\_map}.\mathrm{get} \mathopen{}\left( k \mathclose{}\right) \mid k \in j \mathclose{}\right] \\ \hspace{1em} c \gets \mathopen{}\left[ \mathrm{dashpot\_coefficient\_map}.\mathrm{get} \mathopen{}\left( k \mathclose{}\right) \mid k \in j \mathclose{}\right] \\ \hspace{1em} \mathrm{footing\_zone} \gets \mathopen{}\left[ \textrm{"center"}, \textrm{"y edge"}, \textrm{"x edge"}, \textrm{"corner"} \mathclose{}\right] \\ \hspace{1em} \mathrm{color} \gets \mathopen{}\left[ \textrm{"grey"}, \textrm{"dodgerblue"}, \textrm{"yellow"}, \textrm{"red"} \mathclose{}\right] \\ \hspace{1em} \mathbf{return} \ \mathopen{}\left( \mathrm{footing\_zone}, \mathrm{color}, j, k, c \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
stiffness
|
float
|
Dynamic stiffness for mode j (translation or rotation) |
required |
dashpot_coefficient
|
float
|
Dashpot coefficient for translation (MN-s/m) or rotation (MN-m/rad) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
footing_zone |
str
|
Footing intensity zone description |
color |
Any
|
color |
vibration_mode |
str
|
Vibration mode for dynamic analysis |
stiffness |
float
|
Dynamic stiffness for mode j (translation or rotation) |
dashpot_coefficient |
float
|
Dashpot coefficient for translation (MN-s/m) or rotation (MN-m/rad) |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_natural\_frequency}(T_{flexible}) \\ \hspace{1em} ω \gets \frac{2 \mathrm{np}.\pi}{T_{flexible}} \\ \hspace{1em} \mathbf{return} \ ω \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
structure_flexible_period
|
float
|
Flexible-base period of structure |
required |
Returns:
| Name | Type | Description |
|---|---|---|
natural_frequency |
float
|
Undamped natural vibration frequency |
get_period_lengthening_ratio(
structure_to_soil_stiffness_ratio,
structure_effective_modal_height,
footing_half_width,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_period\_lengthening\_ratio}(h/{V_s\ T}, h, B_h) \\ \hspace{1em} \mathrm{height\_width\_ratio} \gets \frac{h}{B_h} \\ \hspace{1em} T_{flexible}/T \gets \mathrm{ReferenceFigureRegistry}.\mathrm{PeriodLengtheningRatio}.\mathrm{interpolate\_at\_x} \mathopen{}\left( \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ T_{flexible}/T \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
structure_to_soil_stiffness_ratio
|
float
|
Ratio of structure to soil stiffness |
required |
structure_effective_modal_height
|
float
|
Height of center of mass for first-mode shape |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
period_lengthening_ratio |
float
|
Ratio of flexible-base to rigid-base period |
get_pile_cross_swaying_rocking_stiffness(
pile_elasticity_modulus,
pile_moment_of_inertia,
shape_parameter,
subgrade_reaction_modulus_at_diameter,
pile_diameter,
soil_profile_shape="linear",
inhomogeneity_alpha=float("nan"),
inhomogeneity_exponent=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_cross\_swaying\_rocking\_stiffness}(E_p, I_p, μ, k_{sd}, D, \mathrm{soil\_profile\_shape}, a, n) \\ \hspace{1em} K_{hr} \gets \mathrm{float} \mathopen{}\left( \textrm{"nan"} \mathclose{}\right) \\ \hspace{1em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"linear"} \\ \hspace{2em} \mathbf{if} \ a = 1 \\ \hspace{3em} K_{hr} \gets 2 E_p \cdot I_p \cdot μ^{2} \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} K_{hr} \gets E_p \cdot I_p \cdot μ^{2} + \frac{k_{sd}}{16 D \cdot μ^{3}} \cdot \mathopen{}\left( 3 + a \cdot \mathopen{}\left( 4 D \cdot μ - 3 \mathclose{}\right) \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"parabolic"} \\ \hspace{3em} K_{hr} \gets E_p \cdot I_p \cdot μ^{2} + k_{sd} \cdot 2^{\frac{-9 - 3 n}{2}} \cdot \mathopen{}\left( \frac{1}{μ \cdot D} \mathclose{}\right)^{n} \frac{\Gamma \mathopen{}\left( 1 + n \mathclose{}\right)}{μ^{2}} \mathopen{}\left( 2^{\frac{5 + n}{2}} - 4 \cos \mathopen{}\left( \frac{\mathopen{}\left( 1 + n \mathclose{}\right) \mathrm{np}.\pi}{4} \mathclose{}\right) + 4 \sin \mathopen{}\left( \frac{\mathopen{}\left( 1 + n \mathclose{}\right) \mathrm{np}.\pi}{4} \mathclose{}\right) \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ K_{hr} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
pile_moment_of_inertia
|
float
|
Moment of inertia of equivalent solid pile |
required |
shape_parameter
|
float
|
Shape parameter analogous to a wavenumber |
required |
subgrade_reaction_modulus_at_diameter
|
float
|
Subgrade reaction modulus at one pile diameter |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
soil_profile_shape
|
str
|
Shape of soil profile |
'linear'
|
inhomogeneity_alpha
|
float
|
Inhomogeneity alpha parameter |
float('nan')
|
inhomogeneity_exponent
|
float
|
Inhomogeneity exponent for soil |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
pile_cross_swaying_rocking_stiffness |
float
|
Cross-swaying-rocking stiffness of pile |
get_pile_elasticity_modulus_solid_from_tubular_section(
pile_elasticity_modulus,
pile_wall_thickness,
pile_diameter,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_elasticity\_modulus\_solid\_from\_tubular\_section}(E_p, t, D) \\ \hspace{1em} E_p \gets E_p \cdot \mathopen{}\left( 1 - \mathopen{}\left( 1 - \frac{2 t}{D} \mathclose{}\right)^{1} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ E_p \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
pile_wall_thickness
|
float
|
Wall thickness of pile |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_elasticity_modulus |
float
|
Young’s modulus of pile material |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_group\_damping\_ratio}(a_0, j, \mathrm{pile\_group\_configuration}) \\ \hspace{1em} \mathbf{return} \ \mathrm{\_pile\_group\_damping\_ratio\_vec} \mathopen{}\left( \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
pile_group_configuration
|
str
|
Configuration of pile group |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_group_damping_ratio |
float
|
Damping ratio for pile group |
get_pile_group_damping_ratio_scalar(
dimensionless_frequency,
vibration_mode,
pile_group_configuration,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_group\_damping\_ratio\_scalar}(a_0, j, \mathrm{pile\_group\_configuration}) \\ \hspace{1em} \mathbf{if} \ j = \textrm{"y"} \\ \hspace{2em} j \gets \textrm{"x"} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathrm{figure} \gets \mathrm{None} \\ \hspace{1em} \mathbf{if} \ j = \textrm{"x"} \\ \hspace{2em} \mathrm{figure} \gets \mathrm{ReferenceFigureRegistry}.\mathrm{PileGroupDampingRatioX} \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ j = \textrm{"yy"} \\ \hspace{3em} \mathrm{figure} \gets \mathrm{ReferenceFigureRegistry}.\mathrm{PileGroupDampingRatioYY} \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} \mathbf{if} \ j = \textrm{"z"} \\ \hspace{4em} \mathrm{figure} \gets \mathrm{ReferenceFigureRegistry}.\mathrm{PileGroupDampingRatioZ} \\ \hspace{3em} \mathbf{end \ if} \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} β_G \gets \mathrm{figure}.\mathrm{interpolate\_at\_x} \mathopen{}\left( \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ β_G \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
pile_group_configuration
|
str
|
Configuration of pile group |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_group_damping_ratio |
float
|
Damping ratio for pile group |
get_pile_group_efficiency_factor(
dimensionless_frequency,
vibration_mode,
pile_group_configuration,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_group\_efficiency\_factor}(a_0, j, \mathrm{pile\_group\_configuration}) \\ \hspace{1em} \mathbf{return} \ \mathrm{\_pile\_group\_efficiency\_factor} \mathopen{}\left( \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
pile_group_configuration
|
str
|
Configuration of pile group |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_group_efficiency_factor |
float
|
Efficiency factor for pile group |
get_pile_group_efficiency_factor_scalar(
dimensionless_frequency,
vibration_mode,
pile_group_configuration,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_group\_efficiency\_factor\_scalar}(a_0, j, \mathrm{pile\_group\_configuration}) \\ \hspace{1em} \mathbf{if} \ j \in \mathopen{}\left( \textrm{"x and y"}, \textrm{"y"} \mathclose{}\right) \\ \hspace{2em} j \gets \textrm{"x"} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathrm{figure} \gets \mathrm{None} \\ \hspace{1em} \mathbf{if} \ j = \textrm{"x"} \\ \hspace{2em} \mathrm{figure} \gets \mathrm{ReferenceFigureRegistry}.\mathrm{PileGroupEfficiencyFactorX} \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ j = \textrm{"yy"} \\ \hspace{3em} \mathrm{figure} \gets \mathrm{ReferenceFigureRegistry}.\mathrm{PileGroupEfficiencyFactorYY} \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} \mathbf{if} \ j = \textrm{"z"} \\ \hspace{4em} \mathrm{figure} \gets \mathrm{ReferenceFigureRegistry}.\mathrm{PileGroupEfficiencyFactorZ} \\ \hspace{3em} \mathbf{end \ if} \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} EF \gets \mathrm{figure}.\mathrm{interpolate\_at\_x} \mathopen{}\left( \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ EF \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
pile_group_configuration
|
str
|
Configuration of pile group |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_group_efficiency_factor |
float
|
Efficiency factor for pile group |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_moment\_of\_inertia}(D, \mathrm{pile\_shape}) \\ \hspace{1em} I_p \gets \mathrm{float} \mathopen{}\left( \textrm{"nan"} \mathclose{}\right) \\ \hspace{1em} \mathbf{if} \ \mathrm{pile\_shape} \in \mathopen{}\left( \textrm{"tubular"}, \textrm{"circle"} \mathclose{}\right) \\ \hspace{2em} I_p \gets \frac{\mathrm{np}.\pi \cdot D^{4}}{64} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ I_p \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_diameter
|
float
|
Outside diameter of pile |
required |
pile_shape
|
str
|
Shape of pile |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_moment_of_inertia |
float
|
Moment of inertia of equivalent solid pile |
get_pile_rocking_stiffness(
pile_elasticity_modulus,
pile_moment_of_inertia,
shape_parameter,
subgrade_reaction_modulus_at_diameter,
pile_diameter,
soil_profile_shape="linear",
inhomogeneity_alpha=float("nan"),
inhomogeneity_exponent=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_rocking\_stiffness}(E_p, I_p, μ, k_{sd}, D, \mathrm{soil\_profile\_shape}, a, n) \\ \hspace{1em} K_{rr} \gets \mathrm{float} \mathopen{}\left( \textrm{"nan"} \mathclose{}\right) \\ \hspace{1em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"linear"} \\ \hspace{2em} \mathbf{if} \ a = 1 \\ \hspace{3em} K_{rr} \gets 2 E_p \cdot I_p \cdot μ \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} K_{rr} \gets \frac{3}{2} \cdot E_p \cdot I_p \cdot μ + \frac{k_{sd}}{8 D \cdot μ^{4}} \cdot \mathopen{}\left( 1 + a \cdot \mathopen{}\left( D \cdot μ - 1 \mathclose{}\right) \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"parabolic"} \\ \hspace{3em} K_{rr} \gets \frac{3}{2} \cdot E_p \cdot I_p \cdot μ + k_{sd} \cdot 2^{\frac{-9 - 3 n}{2}} \cdot \mathopen{}\left( \frac{1}{μ \cdot D} \mathclose{}\right)^{n} \frac{\Gamma \mathopen{}\left( 1 + n \mathclose{}\right)}{μ^{3}} \mathopen{}\left( 2^{\frac{5 + n}{2}} - 4 \cos \mathopen{}\left( \frac{\mathopen{}\left( 1 + n \mathclose{}\right) \mathrm{np}.\pi}{4} \mathclose{}\right) \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ K_{rr} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
pile_moment_of_inertia
|
float
|
Moment of inertia of equivalent solid pile |
required |
shape_parameter
|
float
|
Shape parameter analogous to a wavenumber |
required |
subgrade_reaction_modulus_at_diameter
|
float
|
Subgrade reaction modulus at one pile diameter |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
soil_profile_shape
|
str
|
Shape of soil profile |
'linear'
|
inhomogeneity_alpha
|
float
|
Inhomogeneity alpha parameter |
float('nan')
|
inhomogeneity_exponent
|
float
|
Inhomogeneity exponent for soil |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
pile_rocking_stiffness |
float
|
Rocking stiffness of pile |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_router}() \\ \hspace{1em} j_{group} \gets \mathopen{}\left[ \textrm{"x and y"}, \textrm{"z"} \mathclose{}\right] \\ \hspace{1em} j \gets \mathopen{}\left[ \textrm{"x"}, \textrm{"z"} \mathclose{}\right] \\ \hspace{1em} \mathrm{foundation\_is\_embedded} \gets \mathopen{}\left[ \mathrm{True}, \mathrm{True} \mathclose{}\right] \\ \hspace{1em} \mathbf{return} \ \mathopen{}\left( j_{group}, j, \mathrm{foundation\_is\_embedded} \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Args:
Returns:
| Name | Type | Description |
|---|---|---|
vibration_mode_group |
str
|
Vibration mode group |
vibration_mode |
str
|
Vibration mode for dynamic analysis |
foundation_is_embedded |
bool
|
Indicates if foundation is embedded |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_stiffness\_in\_group}(EF, k_p) \\ \hspace{1em} k_{pG} \gets EF \cdot k_p \\ \hspace{1em} \mathbf{return} \ k_{pG} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_group_efficiency_factor
|
float
|
Efficiency factor for pile group |
required |
pile_stiffness
|
float
|
Dynamic stiffness of single pile for mode j (translation or rotation) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_stiffness_in_group |
float
|
Dynamic stiffness of pile in group for mode j |
get_pile_swaying_stiffness(
pile_elasticity_modulus,
pile_moment_of_inertia,
shape_parameter,
subgrade_reaction_modulus_at_diameter,
pile_diameter,
soil_profile_shape="linear",
inhomogeneity_alpha=float("nan"),
inhomogeneity_exponent=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_pile\_swaying\_stiffness}(E_p, I_p, μ, k_{sd}, D, \mathrm{soil\_profile\_shape}, a, n) \\ \hspace{1em} K_{hh} \gets \mathrm{float} \mathopen{}\left( \textrm{"nan"} \mathclose{}\right) \\ \hspace{1em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"linear"} \\ \hspace{2em} \mathbf{if} \ a = 1 \\ \hspace{3em} K_{hh} \gets 4 E_p \cdot I_p \cdot μ^{3} \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} K_{hh} \gets E_p \cdot I_p \cdot μ^{3} + \frac{3 k_{sd}}{8 D \cdot μ^{2}} \cdot \mathopen{}\left( 1 + a \cdot \mathopen{}\left( 2 D \cdot μ - 1 \mathclose{}\right) \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"parabolic"} \\ \hspace{3em} K_{hh} \gets E_p \cdot I_p \cdot μ^{3} + k_{sd} \cdot 2^{\frac{-5 - 3 n}{2}} \cdot \mathopen{}\left( \frac{1}{μ \cdot D} \mathclose{}\right)^{n} \frac{\Gamma \mathopen{}\left( 1 + n \mathclose{}\right)}{μ} \mathopen{}\left( 2^{\frac{3 + n}{2}} + 2 \sin \mathopen{}\left( \frac{\mathopen{}\left( 1 + n \mathclose{}\right) \mathrm{np}.\pi}{4} \mathclose{}\right) \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ K_{hh} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
pile_moment_of_inertia
|
float
|
Moment of inertia of equivalent solid pile |
required |
shape_parameter
|
float
|
Shape parameter analogous to a wavenumber |
required |
subgrade_reaction_modulus_at_diameter
|
float
|
Subgrade reaction modulus at one pile diameter |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
soil_profile_shape
|
str
|
Shape of soil profile |
'linear'
|
inhomogeneity_alpha
|
float
|
Inhomogeneity alpha parameter |
float('nan')
|
inhomogeneity_exponent
|
float
|
Inhomogeneity exponent for soil |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
pile_swaying_stiffness |
float
|
Swaying stiffness of pile |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_poisson\_adjustment\_factor}(ν) \\ \hspace{1em} ψ \gets \sqrt{ \frac{2 \mathopen{}\left( 1 - ν \mathclose{}\right)}{1 - 2 ν} } \\ \hspace{1em} ψ \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( ψ, \mathrm{None}, 2.5 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ ψ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
poisson_ratio
|
float
|
Poisson’s ratio of soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
poisson_adjustment_factor |
float
|
Adjustment factor for Poisson’s ratio |
get_radiation_damping_ratio(
shear_modulus,
footing_half_length,
footing_half_width,
dimensionless_frequency,
dynamic_stiffness_modifier,
static_stiffness,
vibration_mode,
foundation_is_embedded=True,
poisson_adjustment_factor=float("nan"),
footing_embedment=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_radiation\_damping\_ratio}(G, L_h, B_h, a_0, α, K, j, \mathrm{foundation\_is\_embedded}, ψ, D_f) \\ \hspace{1em} \mathrm{condition\_1} \gets \mathrm{foundation\_is\_embedded} \mathbin{\&} \mathrm{np}.\mathrm{isin} \mathopen{}\left( j, \mathopen{}\left( \textrm{"x"}, \textrm{"y"} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_1} \gets \frac{4 \frac{L_h}{B_h}}{\frac{K}{G \cdot B_h}} \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_2} \gets \mathrm{foundation\_is\_embedded} \mathbin{\&} \mathopen{}\left( j = \textrm{"z"} \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_2} \gets \frac{4 ψ \frac{L_h}{B_h}}{\frac{K}{G \cdot B_h}} \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_3} \gets \mathrm{foundation\_is\_embedded} \mathbin{\&} \mathopen{}\left( j = \textrm{"xx"} \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_3} \gets \frac{\frac{4 ψ}{3} \frac{L_h}{B_h} \cdot a_0^{2}}{\frac{K}{G \cdot B_h^{3}} \cdot \mathopen{}\left( 2.2 - \frac{0.4}{\mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3}} + a_0^{2} \mathclose{}\right)} \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_4} \gets \mathrm{foundation\_is\_embedded} \mathbin{\&} \mathopen{}\left( j = \textrm{"yy"} \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_4} \gets \frac{\frac{4 ψ}{3} \cdot \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3} a_0^{2}}{\frac{K}{G \cdot B_h^{3}} \cdot \mathopen{}\left( \frac{1.8}{1 + 1.75 \mathopen{}\left( \frac{L_h}{B_h} - 1 \mathclose{}\right)} + a_0^{2} \mathclose{}\right)} \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_5} \gets \mathrm{foundation\_is\_embedded} \mathbin{\&} \mathopen{}\left( j = \textrm{"zz"} \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_5} \gets \frac{\frac{4}{3} \cdot \mathopen{}\left( \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3} + \frac{L_h}{B_h} \mathclose{}\right) a_0^{2}}{\frac{K}{G \cdot B_h^{3}} \cdot \mathopen{}\left( \frac{1.4}{1 + 3 \mathopen{}\left( \frac{L_h}{B_h} - 1 \mathclose{}\right)^{0.7}} + a_0^{2} \mathclose{}\right)} \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_6} \gets j = \textrm{"x"} \\ \hspace{1em} \mathrm{choice\_6} \gets \frac{4 \mathopen{}\left( \frac{L_h}{B_h} + \frac{D_f}{B_h} \cdot \mathopen{}\left( ψ + \frac{L_h}{B_h} \mathclose{}\right) \mathclose{}\right)}{\frac{K}{G \cdot B_h}} \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_7} \gets j = \textrm{"y"} \\ \hspace{1em} \mathrm{choice\_7} \gets \frac{4 \mathopen{}\left( \frac{L_h}{B_h} + \frac{D_f}{B_h} \cdot \mathopen{}\left( 1 + ψ \cdot \frac{L_h}{B_h} \mathclose{}\right) \mathclose{}\right)}{\frac{K}{G \cdot B_h}} \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_8} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_8} \gets \frac{4 \mathopen{}\left( ψ \cdot \frac{L_h}{B_h} + \frac{D_f}{B_h} \cdot \mathopen{}\left( 1 + \frac{L_h}{B_h} \mathclose{}\right) \mathclose{}\right)}{\frac{K}{G \cdot B_h}} \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_9} \gets j = \textrm{"xx"} \\ \hspace{1em} \mathrm{choice\_9} \gets \mathopen{}\left( \frac{\frac{4}{3} \cdot \mathopen{}\left( \frac{D_f}{B_h} + \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{3} + ψ \cdot \frac{L_h}{B_h} \cdot \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{3} + 3 \frac{D_f}{B_h} \frac{L_h}{B_h} + ψ \cdot \frac{L_h}{B_h} \mathclose{}\right) a_0^{2}}{\frac{K}{G \cdot B_h^{3}} \cdot \mathopen{}\left( \frac{1.8}{1 + 1.75 \mathopen{}\left( \frac{L_h}{B_h} - 1 \mathclose{}\right)} + a_0^{2} \mathclose{}\right)} + \frac{\frac{4}{3} \cdot \mathopen{}\left( ψ \cdot \frac{L_h}{B_h} + 1 \mathclose{}\right) \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{3}}{\frac{K}{G \cdot B_h^{3}}} \mathclose{}\right) \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_10} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_10} \gets \mathopen{}\left( \frac{\frac{4}{3} \cdot \mathopen{}\left( \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3} \frac{D_f}{B_h} + ψ \cdot \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{3} \frac{L_h}{B_h} + \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{3} + 3 \frac{D_f}{B_h} \cdot \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{2} + ψ \cdot \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3} \mathclose{}\right) a_0^{2}}{\frac{K}{G \cdot B_h^{3}} \cdot \mathopen{}\left( \frac{1.8}{1 + 1.75 \mathopen{}\left( \frac{L_h}{B_h} - 1 \mathclose{}\right)} + a_0^{2} \mathclose{}\right)} + \frac{\frac{4}{3} \cdot \mathopen{}\left( \frac{L_h}{B_h} + ψ \mathclose{}\right) \mathopen{}\left( \frac{D_f}{B_h} \mathclose{}\right)^{3}}{\frac{K}{G \cdot B_h^{3}}} \mathclose{}\right) \frac{a_0}{2 α} \\ \hspace{1em} \mathrm{condition\_11} \gets j = \textrm{"zz"} \\ \hspace{1em} \mathrm{choice\_11} \gets \frac{\frac{4}{3} \cdot \mathopen{}\left( 3 \frac{L_h}{B_h} \frac{D_f}{B_h} + ψ \cdot \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3} \frac{D_f}{B_h} + 3 \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{2} \frac{D_f}{B_h} + ψ \cdot \frac{D_f}{B_h} + \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{3} + \frac{L_h}{B_h} \mathclose{}\right) a_0^{2}}{\frac{K}{G \cdot B_h^{3}}} \cdot \mathopen{}\left( \frac{1.4}{1 + 3 \mathopen{}\left( \frac{L_h}{B_h} - 1 \mathclose{}\right)^{0.7}} + a_0^{2} \mathclose{}\right) \frac{a_0}{2 α} \\ \hspace{1em} β \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3}, \mathrm{condition\_4}, \mathrm{condition\_5}, \mathrm{condition\_6}, \mathrm{condition\_7}, \mathrm{condition\_8}, \mathrm{condition\_9}, \mathrm{condition\_10}, \mathrm{condition\_11} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3}, \mathrm{choice\_4}, \mathrm{choice\_5}, \mathrm{choice\_6}, \mathrm{choice\_7}, \mathrm{choice\_8}, \mathrm{choice\_9}, \mathrm{choice\_10}, \mathrm{choice\_11} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ β \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
shear_modulus
|
float
|
Shear modulus of soil |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
dynamic_stiffness_modifier
|
float
|
Frequency-dependent stiffness modifier for mode j |
required |
static_stiffness
|
float
|
Static stiffness for mode j (translation or rotation) |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
foundation_is_embedded
|
bool
|
Indicates if foundation is embedded |
True
|
poisson_adjustment_factor
|
float
|
Adjustment factor for Poisson’s ratio |
float('nan')
|
footing_embedment
|
float
|
Depth of footing embedment |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
radiation_damping_ratio |
float
|
Radiation damping ratio for soil |
get_radiation_damping_ratio_rx(
dynamic_stiffness_modifier,
dimensionless_subgrade_reaction_modulus,
poisson_ratio,
dimensionless_frequency,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_radiation\_damping\_ratio\_rx}(α, δ, ν, a_0) \\ \hspace{1em} β \gets \frac{3}{2 α \cdot \mathopen{}\left( 1 + ν \mathclose{}\right) δ} \cdot a_0^{\frac{3}{4}} \\ \hspace{1em} \mathbf{return} \ β \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dynamic_stiffness_modifier
|
float
|
Frequency-dependent stiffness modifier for mode j |
required |
dimensionless_subgrade_reaction_modulus
|
float
|
Dimensionless modulus of subgrade reaction |
required |
poisson_ratio
|
float
|
Poisson’s ratio of soil |
required |
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
radiation_damping_ratio |
float
|
Radiation damping ratio for soil |
get_response_embedment_modification__lizundia2020practical(
footing_embedment,
average_effective_shear_velocity,
period=DEEPSOIL_PERIODS,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_response\_embedment\_modification\_\_lizundia2020practical}(D_f, V_{s,avg}, T) \\ \hspace{1em} T \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( T, 0.2, \mathrm{None} \mathclose{}\right) \\ \hspace{1em} RRS_e \gets 0.25 + 0.75 \cos \mathopen{}\left( \frac{2 \mathrm{np}.\pi \cdot D_f}{T \cdot V_{s,avg}} \mathclose{}\right) \\ \hspace{1em} RRS_e \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( RRS_e, 0.7, \mathrm{None} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ RRS_e \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
footing_embedment
|
float
|
Depth of footing embedment |
required |
average_effective_shear_velocity
|
float
|
Average effective profile velocity |
required |
period
|
float
|
Vibration period of structure or soil |
DEEPSOIL_PERIODS
|
Returns:
| Name | Type | Description |
|---|---|---|
response_embedment_modification |
float
|
Response spectrum modification for embedment |
get_shape_parameter(
active_pile_length,
pile_diameter,
dimensionless_pile_length_parameter,
soil_profile_shape="linear",
inhomogeneity_alpha=None,
inhomogeneity_exponent=None,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_shape\_parameter}(L_a, D, λL, \mathrm{soil\_profile\_shape}, a, n) \\ \hspace{1em} μ \gets \mathrm{float} \mathopen{}\left( \textrm{"nan"} \mathclose{}\right) \\ \hspace{1em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"linear"} \\ \hspace{2em} \mathbf{if} \ a = 1 \\ \hspace{3em} μ \gets λL \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} μ \gets \frac{4 λL}{5 D^{\frac{1}{4}} \cdot L_a \cdot \mathopen{}\left( a - 1 \mathclose{}\right)} \mathopen{}\left( \mathopen{}\left( a \cdot D \mathclose{}\right)^{\frac{5}{4}} - \mathopen{}\left( a \cdot D - a \cdot L_a + L_a \mathclose{}\right)^{\frac{5}{4}} \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ \mathrm{soil\_profile\_shape} = \textrm{"parabolic"} \\ \hspace{3em} μ \gets \frac{4}{4 + n} \cdot \mathopen{}\left( \frac{L_a}{D} \mathclose{}\right)^{\frac{n}{4}} λL \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ μ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
active_pile_length
|
float
|
Active pile length in lateral mode (typically < L_p) |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
dimensionless_pile_length_parameter
|
float
|
Dimensionless pile length parameter |
required |
soil_profile_shape
|
str
|
Shape of soil profile |
'linear'
|
inhomogeneity_alpha
|
float
|
Inhomogeneity alpha parameter |
None
|
inhomogeneity_exponent
|
float
|
Inhomogeneity exponent for soil |
None
|
Returns:
| Name | Type | Description |
|---|---|---|
shape_parameter |
float
|
Shape parameter analogous to a wavenumber |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_square\_equivalent\_circle\_diameter}(D) \\ \hspace{1em} D \gets 2 \mathopen{}\left( \frac{D^{2}}{\mathrm{np}.\pi} \mathclose{}\right)^{0.5} \\ \hspace{1em} \mathbf{return} \ D \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_diameter
|
float
|
Outside diameter of pile |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_diameter |
float
|
Outside diameter of pile |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_ssi\_effects\_expected}(h/{V_s\ T}) \\ \hspace{1em} \mathrm{ssi\_effects\_expected} \gets h/{V_s\ T} > 0.1 \\ \hspace{1em} \mathbf{return} \ \mathrm{ssi\_effects\_expected} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
structure_to_soil_stiffness_ratio
|
float
|
Ratio of structure to soil stiffness |
required |
Returns:
| Name | Type | Description |
|---|---|---|
ssi_effects_expected |
bool
|
Indicates expected soil-structure interaction effects |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_static\_pile\_stiffness}(E_s, D, χ) \\ \hspace{1em} K \gets χ \cdot E_s \cdot D \\ \hspace{1em} \mathbf{return} \ K \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
elasticity_modulus
|
float
|
Modulus of elasticity of soil |
required |
pile_diameter
|
float
|
Outside diameter of pile |
required |
vibration_constant
|
float
|
Dimensionless constant for vibration for mode j |
required |
Returns:
| Name | Type | Description |
|---|---|---|
static_stiffness |
float
|
Static stiffness for mode j (translation or rotation) |
get_static_stiffness(
shear_modulus,
footing_half_length,
footing_half_width,
vibration_mode,
foundation_is_embedded,
poisson_ratio=float("nan"),
embedment_factor=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_static\_stiffness}(G, L_h, B_h, j, \mathrm{foundation\_is\_embedded}, ν, η) \\ \hspace{1em} \mathrm{condition\_1} \gets j = \textrm{"x"} \\ \hspace{1em} \mathrm{choice\_1} \gets \frac{G \cdot B_h}{2 - ν} \cdot \mathopen{}\left( 6.8 \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{0.65} + 2.4 \mathclose{}\right) \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"y"} \\ \hspace{1em} \mathrm{choice\_2} \gets \frac{G \cdot B_h}{2 - ν} \cdot \mathopen{}\left( 6.8 \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{0.65} + 0.8 \frac{L_h}{B_h} + 1.6 \mathclose{}\right) \\ \hspace{1em} \mathrm{condition\_3} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_3} \gets \frac{G \cdot B_h}{1 - ν} \cdot \mathopen{}\left( 3.1 \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{0.75} + 1.6 \mathclose{}\right) \\ \hspace{1em} \mathrm{condition\_4} \gets j = \textrm{"xx"} \\ \hspace{1em} \mathrm{choice\_4} \gets \frac{G \cdot B_h^{3}}{1 - ν} \cdot \mathopen{}\left( 3.2 \frac{L_h}{B_h} + 0.8 \mathclose{}\right) \\ \hspace{1em} \mathrm{condition\_5} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_5} \gets \frac{G \cdot B_h^{3}}{1 - ν} \cdot \mathopen{}\left( 3.73 \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{2.4} + 0.27 \mathclose{}\right) \\ \hspace{1em} \mathrm{condition\_6} \gets j = \textrm{"zz"} \\ \hspace{1em} \mathrm{choice\_6} \gets G \cdot B_h^{3} \cdot \mathopen{}\left( 4.25 \mathopen{}\left( \frac{L_h}{B_h} \mathclose{}\right)^{2.45} + 4.06 \mathclose{}\right) \\ \hspace{1em} K \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3}, \mathrm{condition\_4}, \mathrm{condition\_5}, \mathrm{condition\_6} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3}, \mathrm{choice\_4}, \mathrm{choice\_5}, \mathrm{choice\_6} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} K \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathord{\sim} \mathrm{foundation\_is\_embedded}, K \cdot η, K \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ K \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
shear_modulus
|
float
|
Shear modulus of soil |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
foundation_is_embedded
|
bool
|
Indicates if foundation is embedded |
required |
poisson_ratio
|
float
|
Poisson’s ratio of soil |
float('nan')
|
embedment_factor
|
float
|
Embedment correction factor for rigid footing spring constants |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
static_stiffness |
float
|
Static stiffness for mode j (translation or rotation) |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stiffness}(α, K) \\ \hspace{1em} k \gets α \cdot K \\ \hspace{1em} \mathbf{return} \ k \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dynamic_stiffness_modifier
|
float
|
Frequency-dependent stiffness modifier for mode j |
required |
static_stiffness
|
float
|
Static stiffness for mode j (translation or rotation) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
stiffness |
float
|
Dynamic stiffness for mode j (translation or rotation) |
get_stiffness_edge_factor(
end_length_ratio,
stiffness,
vertical_stiffness_intensity,
footing_half_width,
footing_half_length,
vibration_mode,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stiffness\_edge\_factor}(R_e, k, k_z^i, B_h, L_h, j) \\ \hspace{1em} \mathrm{condition\_1} \gets \mathopen{}\left( R_e = 0 \mathclose{}\right) \mathbin{\&} \mathopen{}\left( j = \textrm{"xx"} \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_1} \gets 0 \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"xx"} \\ \hspace{1em} \mathrm{choice\_2} \gets \frac{\frac{3 k}{4 k_z^i \cdot B_h^{3} \cdot L_h} - \mathopen{}\left( 1 - R_e \mathclose{}\right)^{3}}{1 - \mathopen{}\left( 1 - R_e \mathclose{}\right)^{3}} \\ \hspace{1em} \mathrm{condition\_3} \gets \mathopen{}\left( R_e = 0 \mathclose{}\right) \mathbin{\&} \mathopen{}\left( j = \textrm{"yy"} \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_3} \gets 0 \\ \hspace{1em} \mathrm{condition\_4} \gets j = \textrm{"yy"} \\ \hspace{1em} \mathrm{choice\_4} \gets \frac{\frac{3 k}{4 k_z^i \cdot B_h \cdot L_h^{3}} - \mathopen{}\left( 1 - R_e \mathclose{}\right)^{3}}{1 - \mathopen{}\left( 1 - R_e \mathclose{}\right)^{3}} \\ \hspace{1em} \mathrm{condition\_5} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_5} \gets 1 \\ \hspace{1em} R_k \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3}, \mathrm{condition\_4}, \mathrm{condition\_5} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3}, \mathrm{choice\_4}, \mathrm{choice\_5} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ R_k \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
end_length_ratio
|
float
|
End length ratio |
required |
stiffness
|
float
|
Dynamic stiffness for mode j (translation or rotation) |
required |
vertical_stiffness_intensity
|
float
|
Vertical stiffness intensity for foundation |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
stiffness_edge_factor |
float
|
Stiffness edge increase factor |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stiffness\_intensity}(k_z^i, R_k) \\ \hspace{1em} k_i \gets k_z^i \cdot R_k \\ \hspace{1em} \mathbf{return} \ k_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
vertical_stiffness_intensity
|
float
|
Vertical stiffness intensity for foundation |
required |
stiffness_edge_factor
|
float
|
Stiffness edge increase factor |
required |
Returns:
| Name | Type | Description |
|---|---|---|
stiffness_intensity |
float
|
Stiffness intensity for foundation |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stiffness\_weight\_factor\_pile\_tip\_x}() \\ \hspace{1em} w_b \gets 0.0 \\ \hspace{1em} \mathbf{return} \ w_b \\ \mathbf{end \ function} \end{array}
\]
Args:
Returns:
| Name | Type | Description |
|---|---|---|
stiffness_weight_factor_pile_tip |
float
|
Weight factor for pile tip stiffness contribution |
get_stiffness_weight_factor_pile_tip_z(
dimensionless_pile_length_parameter,
dimensionless_pile_tip_stiffness,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stiffness\_weight\_factor\_pile\_tip\_z}(λL, Ω) \\ \hspace{1em} w_b \gets \frac{2 Ω}{2 Ω \cdot \cosh λL \cdot \mathopen{}\left( 1 + Ω^{2} \mathclose{}\right) \sinh λL} \\ \hspace{1em} \mathbf{return} \ w_b \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_pile_length_parameter
|
float
|
Dimensionless pile length parameter |
required |
dimensionless_pile_tip_stiffness
|
float
|
Dimensionless pile tip stiffness |
required |
Returns:
| Name | Type | Description |
|---|---|---|
stiffness_weight_factor_pile_tip |
float
|
Weight factor for pile tip stiffness contribution |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stiffness\_weight\_factor\_pile\_x}() \\ \hspace{1em} w_p \gets \frac{1}{4} \\ \hspace{1em} \mathbf{return} \ w_p \\ \mathbf{end \ function} \end{array}
\]
Args:
Returns:
| Name | Type | Description |
|---|---|---|
stiffness_weight_factor_pile |
float
|
Weight factor for pile stiffness contribution |
get_stiffness_weight_factor_pile_z(
stiffness_weight_factor_soil,
stiffness_weight_factor_pile_tip,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stiffness\_weight\_factor\_pile\_z}(w_s, w_b) \\ \hspace{1em} w_p \gets 1 - \mathopen{}\left( w_s + w_b \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ w_p \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
stiffness_weight_factor_soil
|
float
|
Weight factor for soil stiffness contribution |
required |
stiffness_weight_factor_pile_tip
|
float
|
Weight factor for pile tip stiffness contribution |
required |
Returns:
| Name | Type | Description |
|---|---|---|
stiffness_weight_factor_pile |
float
|
Weight factor for pile stiffness contribution |
get_stiffness_weight_factor_soil(
dimensionless_pile_length_parameter,
dimensionless_pile_tip_stiffness,
vibration_mode,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stiffness\_weight\_factor\_soil}(λL, Ω, j) \\ \hspace{1em} \mathrm{condition\_1} \gets j = \textrm{"x"} \\ \hspace{1em} \mathrm{choice\_1} \gets \frac{3}{4} \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_2} \gets \frac{-2 \mathopen{}\left( λL \cdot \mathopen{}\left( Ω^{2} - 1 \mathclose{}\right) + Ω \mathclose{}\right) + 2 Ω \cdot \cosh \mathopen{}\left( 2 λL \mathclose{}\right) + \mathopen{}\left( 1 + Ω^{2} \mathclose{}\right) \sinh \mathopen{}\left( 2 λL \mathclose{}\right)}{4 \mathopen{}\left( \cosh λL \mathclose{}\right)^{2} \mathopen{}\left( Ω + \tanh λL \mathclose{}\right) \mathopen{}\left( 1 + Ω \cdot \tanh λL \mathclose{}\right)} \\ \hspace{1em} w_s \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ w_s \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_pile_length_parameter
|
float
|
Dimensionless pile length parameter |
required |
dimensionless_pile_tip_stiffness
|
float
|
Dimensionless pile tip stiffness |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
stiffness_weight_factor_soil |
float
|
Weight factor for soil stiffness contribution |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_structure\_effective\_modal\_height}(h_{total}) \\ \hspace{1em} h \gets \frac{2}{3} \cdot h_{total} \\ \hspace{1em} \mathbf{return} \ h \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
structure_total_height
|
float
|
Building height from foundation to roof |
required |
Returns:
| Name | Type | Description |
|---|---|---|
structure_effective_modal_height |
float
|
Height of center of mass for first-mode shape |
get_structure_to_soil_stiffness_ratio(
structure_effective_modal_height,
average_effective_shear_velocity,
structure_rigid_period,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_structure\_to\_soil\_stiffness\_ratio}(h, V_{s,avg}, T) \\ \hspace{1em} h/{V_s\ T} \gets \frac{h}{V_{s,avg} \cdot T} \\ \hspace{1em} \mathbf{return} \ h/{V_s\ T} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
structure_effective_modal_height
|
float
|
Height of center of mass for first-mode shape |
required |
average_effective_shear_velocity
|
float
|
Average effective profile velocity |
required |
structure_rigid_period
|
float
|
Undamped natural vibration period of structure |
required |
Returns:
| Name | Type | Description |
|---|---|---|
structure_to_soil_stiffness_ratio |
float
|
Ratio of structure to soil stiffness |
get_subgrade_reaction_modulus_at_diameter(
dimensionless_subgrade_reaction_modulus,
elasticity_modulus,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_subgrade\_reaction\_modulus\_at\_diameter}(δ, E_s) \\ \hspace{1em} k_{sd} \gets δ \cdot E_s \\ \hspace{1em} \mathbf{return} \ k_{sd} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
dimensionless_subgrade_reaction_modulus
|
float
|
Dimensionless modulus of subgrade reaction |
required |
elasticity_modulus
|
float
|
Modulus of elasticity of soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
subgrade_reaction_modulus_at_diameter |
float
|
Subgrade reaction modulus at one pile diameter |
get_vertical_stiffness_intensity(
vibration_mode,
stiffness,
footing_half_width,
footing_half_length,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_vertical\_stiffness\_intensity}(j, k, B_h, L_h) \\ \hspace{1em} \mathrm{stiffness\_map} \gets \mathrm{dict} \mathopen{}\left( \mathrm{zip} \mathopen{}\left( \mathrm{np}.\mathrm{atleast\_1d} \mathopen{}\left( j \mathclose{}\right), \mathrm{np}.\mathrm{atleast\_1d} \mathopen{}\left( k \mathclose{}\right) \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} k_z \gets \mathrm{stiffness\_map}_{\textrm{"z"}} \\ \hspace{1em} k_z^i \gets \frac{k_z}{4 B_h \cdot L_h} \\ \hspace{1em} \mathbf{return} \ k_z^i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
stiffness
|
float
|
Dynamic stiffness for mode j (translation or rotation) |
required |
footing_half_width
|
float
|
Footing half-width (small plan dimension) |
required |
footing_half_length
|
float
|
Footing half-length (large plan dimension) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
vertical_stiffness_intensity |
float
|
Vertical stiffness intensity for foundation |
get_vibration_constant(
pile_elasticity_modulus,
elasticity_modulus,
dimensionless_subgrade_reaction_modulus,
vibration_mode,
dimensionless_pile_length_parameter=float("nan"),
dimensionless_pile_tip_stiffness=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_vibration\_constant}(E_p, E_s, δ, j, λL, Ω) \\ \hspace{1em} \mathrm{condition\_1} \gets j = \textrm{"x"} \\ \hspace{1em} \mathrm{choice\_1} \gets \frac{1}{2} \cdot \mathrm{np}.\pi^{\frac{1}{4}} \cdot δ^{\frac{3}{4}} \cdot \mathopen{}\left( \frac{E_p}{E_s} \mathclose{}\right)^{\frac{1}{4}} \\ \hspace{1em} \mathrm{condition\_2} \gets j = \textrm{"z"} \\ \hspace{1em} \mathrm{choice\_2} \gets \mathopen{}\left( \frac{\mathrm{np}.\pi \cdot δ}{2} \mathclose{}\right)^{\frac{1}{2}} \mathopen{}\left( \frac{E_p}{E_s} \mathclose{}\right)^{\frac{1}{2}} \frac{Ω + \tanh λL}{1 + Ω \cdot \tanh λL} \\ \hspace{1em} χ \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ χ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
pile_elasticity_modulus
|
float
|
Young’s modulus of pile material |
required |
elasticity_modulus
|
float
|
Modulus of elasticity of soil |
required |
dimensionless_subgrade_reaction_modulus
|
float
|
Dimensionless modulus of subgrade reaction |
required |
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
dimensionless_pile_length_parameter
|
float
|
Dimensionless pile length parameter |
float('nan')
|
dimensionless_pile_tip_stiffness
|
float
|
Dimensionless pile tip stiffness |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
vibration_constant |
float
|
Dimensionless constant for vibration for mode j |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{pile\_group\_router}(j, a_0, k) \\ \hspace{1em} \mathrm{pile\_group\_configuration} \gets \mathopen{}\left[ \textrm{"2X2"}, \textrm{"2X2"}, \textrm{"3X3"}, \textrm{"3X3"}, \textrm{"4X4"}, \textrm{"4X4"} \mathclose{}\right] \\ \hspace{1em} j \gets \mathrm{np}.\mathrm{tile} \mathopen{}\left( j, 3 \mathclose{}\right) \\ \hspace{1em} a_0 \gets \mathrm{np}.\mathrm{tile} \mathopen{}\left( a_0, 3 \mathclose{}\right) \\ \hspace{1em} k \gets \mathrm{np}.\mathrm{tile} \mathopen{}\left( k, 3 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ \mathopen{}\left( \mathrm{pile\_group\_configuration}, j, a_0, k \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
vibration_mode
|
str
|
Vibration mode for dynamic analysis |
required |
dimensionless_frequency
|
float
|
Dimensionless frequency for dynamic analysis |
required |
stiffness
|
float
|
Dynamic stiffness for mode j (translation or rotation) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
pile_group_configuration |
str
|
Configuration of pile group |
vibration_mode |
str
|
Vibration mode for dynamic analysis |
dimensionless_frequency |
float
|
Dimensionless frequency for dynamic analysis |
pile_stiffness |
float
|
Dynamic stiffness of single pile for mode j (translation or rotation) |