liquefaction.py
Liquefaction functions.
Classes:
| Name | Description |
|---|---|
ReferenceFigureRegistry |
Pre-instantiated reference figures |
Functions:
Pre-instantiated reference figures
get_area_replacement_ratio(
stone_column_arrangement,
stone_column_diameter=float("nan"),
stone_column_spacing=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_area\_replacement\_ratio}(\mathrm{stone\_column\_arrangement}, D, S) \\ \hspace{1em} \mathbf{if} \ \mathrm{stone\_column\_arrangement} = \textrm{"triangular"} \\ \hspace{2em} A_r \gets 0.907 \mathopen{}\left( \frac{D}{S} \mathclose{}\right)^{2} \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ \mathrm{stone\_column\_arrangement} = \textrm{"rectangular"} \\ \hspace{3em} A_r \gets \mathrm{np}.\pi \cdot \mathopen{}\left( \frac{0.5 D}{S} \mathclose{}\right)^{2} \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} A_r \gets \mathrm{float} \mathopen{}\left( \textrm{"nan"} \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ A_r \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
stone_column_arrangement
|
str
|
Arrangement of stone columns |
required |
stone_column_diameter
|
float
|
Diameter of stone column |
float('nan')
|
stone_column_spacing
|
float
|
Spacing between stone columns |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
area_replacement_ratio |
float
|
Ratio of one column area to the unit cell area |
get_cyclic_resistance_ratio(
cyclic_resistance_ratio_magnitude_7_5,
magnitude_scaling_factor,
overburden_correction_crr,
initial_static_shear_correction,
is_potentially_liquefiable,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_cyclic\_resistance\_ratio}(CRR_{7.5}, MSF, K_σ, K_α, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} CRR \gets CRR_{7.5} \cdot K_σ \cdot K_α \cdot MSF \\ \hspace{1em} CRR \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( CRR, \mathrm{None}, 2 \mathclose{}\right) \\ \hspace{1em} CRR \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathrm{np}.\mathrm{isnan} \mathopen{}\left( CRR \mathclose{}\right) \mathbin{|} \mathord{\sim} \mathrm{is\_potentially\_liquefiable}, 2, CRR \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ CRR \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
cyclic_resistance_ratio_magnitude_7_5
|
float
|
Cyclic resistance ratio adjusted to moment magnitude 7.5 |
required |
magnitude_scaling_factor
|
float
|
Magnitude scaling factor for liquefaction |
required |
overburden_correction_crr
|
float
|
Overburden correction factor for cyclic resistance ratio |
required |
initial_static_shear_correction
|
float
|
Correction for initial static shear stress ratio |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
cyclic_resistance_ratio |
float
|
Cyclic resistance ratio for liquefaction |
get_cyclic_resistance_ratio__cetin2004standard(
normalized_blow_count,
effective_stress,
fines_content,
moment_magnitude,
is_potentially_liquefiable,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_cyclic\_resistance\_ratio\_\_cetin2004standard}(N_{160}, σ_v', FC, M_w, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} PL_{liq} \gets 50 \\ \hspace{1em} \mathopen{}\left( \mathrm{theta1}, \mathrm{theta2}, \mathrm{theta3}, \mathrm{theta4}, \mathrm{theta5}, \mathrm{theta6}, \mathrm{theta\_epsilon} \mathclose{}\right) \gets \mathrm{list} \mathopen{}\left( \mathrm{ReferenceDataSets}.\mathrm{ModelCoefficientsCetin}.\mathrm{to\_index\_map} \mathopen{}\left( \textrm{"theta"}, \textrm{"2004"} \mathclose{}\right).\mathrm{values} \mathopen{}\left( \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} CRR \gets \exp \mathopen{}\left( \frac{N_{160} \cdot \mathopen{}\left( 1 + \mathrm{theta1} \cdot FC \mathclose{}\right) - \mathrm{theta2} \cdot \log M_w - \mathrm{theta3} \cdot \log \mathopen{}\left( \frac{σ_v'}{101.325} \mathclose{}\right) + \mathrm{theta4} \cdot FC + \mathrm{theta5} + \mathrm{theta\_epsilon} \cdot \mathrm{norm} \mathopen{}\left( \mathclose{}\right).\mathrm{ppf} \mathopen{}\left( \frac{PL_{liq}}{100} \mathclose{}\right)}{\mathrm{theta6}} \mathclose{}\right) \\ \hspace{1em} CRR \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathrm{np}.\mathrm{isnan} \mathopen{}\left( CRR \mathclose{}\right) \mathbin{|} \mathord{\sim} \mathrm{is\_potentially\_liquefiable}, 2, CRR \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ CRR \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
normalized_blow_count
|
float
|
N_60 corrected to 1 atm effective overburden stress |
required |
effective_stress
|
float
|
Effective vertical stress in soil |
required |
fines_content
|
float
|
Percentage of fines passing No. 200 sieve |
required |
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
cyclic_resistance_ratio |
float
|
Cyclic resistance ratio for liquefaction |
get_cyclic_resistance_ratio__cetin2018use(
normalized_blow_count,
effective_stress,
fines_content,
moment_magnitude,
is_potentially_liquefiable,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_cyclic\_resistance\_ratio\_\_cetin2018use}(N_{160}, σ_v', FC, M_w, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} PL_{liq} \gets 50 \\ \hspace{1em} \mathopen{}\left( \mathrm{theta1}, \mathrm{theta2}, \mathrm{theta3}, \mathrm{theta4}, \mathrm{theta5}, \mathrm{theta6}, \mathrm{theta\_epsilon} \mathclose{}\right) \gets \mathrm{list} \mathopen{}\left( \mathrm{ReferenceDataSets}.\mathrm{ModelCoefficientsCetin}.\mathrm{to\_index\_map} \mathopen{}\left( \textrm{"theta"}, \textrm{"2018"} \mathclose{}\right).\mathrm{values} \mathopen{}\left( \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} CRR \gets \exp \mathopen{}\left( \frac{N_{160} \cdot \mathopen{}\left( 1 + \mathrm{theta1} \cdot FC \mathclose{}\right) - \mathrm{theta2} \cdot \log M_w - \mathrm{theta3} \cdot \log \mathopen{}\left( \frac{σ_v'}{101.325} \mathclose{}\right) + \mathrm{theta4} \cdot FC + \mathrm{theta5} + \mathrm{theta\_epsilon} \cdot \mathrm{norm} \mathopen{}\left( \mathclose{}\right).\mathrm{ppf} \mathopen{}\left( \frac{PL_{liq}}{100} \mathclose{}\right)}{\mathrm{theta6}} \mathclose{}\right) \\ \hspace{1em} CRR \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathrm{np}.\mathrm{isnan} \mathopen{}\left( CRR \mathclose{}\right) \mathbin{|} \mathord{\sim} \mathrm{is\_potentially\_liquefiable}, 2, CRR \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ CRR \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
normalized_blow_count
|
float
|
N_60 corrected to 1 atm effective overburden stress |
required |
effective_stress
|
float
|
Effective vertical stress in soil |
required |
fines_content
|
float
|
Percentage of fines passing No. 200 sieve |
required |
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
cyclic_resistance_ratio |
float
|
Cyclic resistance ratio for liquefaction |
get_cyclic_resistance_ratio__saye2021common(
cyclic_resistance_ratio_magnitude_7_5,
magnitude_scaling_factor,
is_potentially_liquefiable,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_cyclic\_resistance\_ratio\_\_saye2021common}(CRR_{7.5}, MSF, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} K_σ \gets 1.0 \\ \hspace{1em} K_α \gets 1.0 \\ \hspace{1em} \mathbf{return} \ \mathrm{get\_cyclic\_resistance\_ratio} \mathopen{}\left( \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
cyclic_resistance_ratio_magnitude_7_5
|
float
|
Cyclic resistance ratio adjusted to moment magnitude 7.5 |
required |
magnitude_scaling_factor
|
float
|
Magnitude scaling factor for liquefaction |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
cyclic_resistance_ratio |
float
|
Cyclic resistance ratio for liquefaction |
get_cyclic_resistance_ratio_magnitude_7_5__cetin2018use(
cyclic_resistance_ratio,
magnitude_scaling_factor,
overburden_correction_crr,
initial_static_shear_correction,
is_potentially_liquefiable,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_cyclic\_resistance\_ratio\_magnitude\_7\_5\_\_cetin2018use}(CRR, MSF, K_σ, K_α, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} CRR_{7.5} \gets \frac{CRR}{K_σ \cdot K_α \cdot MSF} \\ \hspace{1em} CRR_{7.5} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( CRR_{7.5}, \mathrm{None}, 2 \mathclose{}\right) \\ \hspace{1em} CRR_{7.5} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathrm{np}.\mathrm{isnan} \mathopen{}\left( CRR_{7.5} \mathclose{}\right) \mathbin{|} \mathord{\sim} \mathrm{is\_potentially\_liquefiable}, 2, CRR_{7.5} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ CRR_{7.5} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
cyclic_resistance_ratio
|
float
|
Cyclic resistance ratio for liquefaction |
required |
magnitude_scaling_factor
|
float
|
Magnitude scaling factor for liquefaction |
required |
overburden_correction_crr
|
float
|
Overburden correction factor for cyclic resistance ratio |
required |
initial_static_shear_correction
|
float
|
Correction for initial static shear stress ratio |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
cyclic_resistance_ratio_magnitude_7_5 |
float
|
Cyclic resistance ratio adjusted to moment magnitude 7.5 |
get_cyclic_resistance_ratio_magnitude_7_5_spt__idriss2006semi(
clean_sand_normalized_blow_count,
is_potentially_liquefiable,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_cyclic\_resistance\_ratio\_magnitude\_7\_5\_spt\_\_idriss2006semi}(N_{160cs}, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} CRR_{7.5} \gets \exp \mathopen{}\left( \frac{N_{160cs}}{14.1} + \mathopen{}\left( \frac{N_{160cs}}{126} \mathclose{}\right)^{2} - \mathopen{}\left( \frac{N_{160cs}}{23.6} \mathclose{}\right)^{3} + \mathopen{}\left( \frac{N_{160cs}}{25.4} \mathclose{}\right)^{4} - 2.8 \mathclose{}\right) \\ \hspace{1em} CRR_{7.5} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathopen{}\left( N_{160cs} \ge 37.5 \mathclose{}\right) \mathbin{|} \mathrm{np}.\mathrm{isnan} \mathopen{}\left( CRR_{7.5} \mathclose{}\right) \mathbin{|} \mathord{\sim} \mathrm{is\_potentially\_liquefiable}, 2, CRR_{7.5} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ CRR_{7.5} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
clean_sand_normalized_blow_count
|
float
|
Equivalent clean sand SPT blow count (N_160) |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
cyclic_resistance_ratio_magnitude_7_5 |
float
|
Cyclic resistance ratio adjusted to moment magnitude 7.5 |
get_cyclic_stress_ratio(
peak_ground_acceleration,
total_stress,
effective_stress,
shear_stress_reduction_coefficient,
stone_column_is_present=False,
shear_stress_reduction_factor=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_cyclic\_stress\_ratio}(PGA, σ_v, σ_v', r_d, sc_{present}, K_G) \\ \hspace{1em} CSR \gets 0.65 PGA \frac{σ_v}{σ_v'} \cdot r_d \\ \hspace{1em} CSR \gets \mathrm{np}.\mathrm{asarray} \mathopen{}\left( CSR \mathclose{}\right) \\ \hspace{1em} sc_{present} \gets \mathrm{np}.\mathrm{broadcast\_to} \mathopen{}\left( sc_{present}, CSR.\mathrm{shape} \mathclose{}\right) \\ \hspace{1em} \mathrm{np}.\mathrm{putmask} \mathopen{}\left( CSR, sc_{present}, CSR \cdot K_G \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ CSR \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
peak_ground_acceleration
|
float
|
Peak ground acceleration for seismic analysis |
required |
total_stress
|
float
|
Total vertical stress in soil |
required |
effective_stress
|
float
|
Effective vertical stress in soil |
required |
shear_stress_reduction_coefficient
|
float
|
Shear stress reduction coefficient for liquefaction |
required |
stone_column_is_present
|
bool
|
Indicates presence of stone column |
False
|
shear_stress_reduction_factor
|
float
|
Shear stress reduction factor for stone columns |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
cyclic_stress_ratio |
float
|
Cyclic stress ratio for liquefaction |
get_cyclic_stress_ratio_ss_20_1d_1atm__cetin2009probabilistica(
cyclic_stress_ratio,
overburden_correction_crr,
membrane_compliance_correction,
triaxial_planes_correction,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_cyclic\_stress\_ratio\_ss\_20\_1d\_1atm\_\_cetin2009probabilistica}(CSR, K_σ, K_{mc}, K_r) \\ \hspace{1em} CSR_{SS,20,1D,1atm} \gets CSR \cdot K_σ \cdot K_{mc} \cdot K_r \\ \hspace{1em} \mathbf{return} \ CSR_{SS,20,1D,1atm} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
cyclic_stress_ratio
|
float
|
Cyclic stress ratio for liquefaction |
required |
overburden_correction_crr
|
float
|
Overburden correction factor for cyclic resistance ratio |
required |
membrane_compliance_correction
|
float
|
Correction factor for membrane compliance in DMT |
required |
triaxial_planes_correction
|
float
|
Correction for shearing of incorrect planes in cyclic triaxial test |
required |
Returns:
| Name | Type | Description |
|---|---|---|
cyclic_stress_ratio_ss_20_1d_1atm |
float
|
CSR value corresponding to a 1 dimensional, 20 uniform loading cycles simple shear test under a confinement pressure of 1 atm |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_initial\_static\_shear\_correction}() \\ \hspace{1em} K_α \gets 1.0 \\ \hspace{1em} \mathbf{return} \ K_α \\ \mathbf{end \ function} \end{array}
\]
Args:
Returns:
| Name | Type | Description |
|---|---|---|
initial_static_shear_correction |
float
|
Correction for initial static shear stress ratio |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_is\_potentially\_liquefiable}(\mathrm{below\_water\_table}, z, LIQ_{max\ z}) \\ \hspace{1em} \mathbf{if} \ \mathrm{np}.\mathrm{isnan} \mathopen{}\left( LIQ_{max\ z} \mathclose{}\right) \\ \hspace{2em} LIQ_{max\ z} \gets \mathrm{np}.\mathrm{inf} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathrm{is\_potentially\_liquefiable} \gets \mathrm{below\_water\_table} \mathbin{\&} \mathopen{}\left( z \le LIQ_{max\ z} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ \mathrm{is\_potentially\_liquefiable} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
below_water_table
|
bool
|
Indicates if soil layer is below water table |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
liquefaction_max_depth
|
float
|
Maximum depth for liquefaction analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
is_potentially_liquefiable |
bool
|
Indicates if soil is potentially liquefiable |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_is\_potentially\_liquefiable\_thickness}(H, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} \textrm{" calculated as the consecutive runs of potentially liquefiable layers thickness "} \\ \hspace{1em} \mathbf{if} \ \mathrm{np}.\mathrm{ndim} \mathopen{}\left( \mathrm{is\_potentially\_liquefiable} \mathclose{}\right) = 0 \\ \hspace{2em} \mathbf{return} \ \left\{ \begin{array}{ll} H, & \mathrm{if} \ \mathrm{is\_potentially\_liquefiable} \\ 0, & \mathrm{otherwise} \end{array} \right. \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathrm{is\_potentially\_liquefiable\_thickness} \gets \mathrm{np}.\mathrm{zeros\_like} \mathopen{}\left( H \mathclose{}\right) \\ \hspace{1em} \mathopen{}\left( \mathrm{run\_values}, \mathrm{run\_starts}, \mathrm{run\_lengths} \mathclose{}\right) \gets \mathrm{find\_runs} \mathopen{}\left( \mathrm{is\_potentially\_liquefiable} \mathclose{}\right) \\ \hspace{1em} \mathbf{for} \ \mathopen{}\left( \mathrm{value}, \mathrm{starts}, \mathrm{length} \mathclose{}\right) \in \mathrm{zip} \mathopen{}\left( \mathrm{run\_values}, \mathrm{run\_starts}, \mathrm{run\_lengths} \mathclose{}\right) \ \mathbf{do} \\ \hspace{2em} \mathbf{if} \ \mathrm{value} \\ \hspace{3em} \mathrm{ends} \gets \mathrm{starts} + \mathrm{length} \\ \hspace{3em} \mathrm{indices} \gets \mathrm{np}.\mathrm{arange} \mathopen{}\left( \mathrm{starts}, \mathrm{ends} \mathclose{}\right) \\ \hspace{3em} \mathrm{is\_potentially\_liquefiable\_thickness}_{\mathrm{indices}} \gets \sum \mathrm{thickness}_{\mathrm{indices}} \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ for} \\ \hspace{1em} \mathbf{return} \ \mathrm{is\_potentially\_liquefiable\_thickness} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
thickness
|
float
|
Thickness of soil layer |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
is_potentially_liquefiable_thickness |
float
|
Thickness of potentially liquefiable group |
get_is_t15_liquefiable_layers(
is_potentially_liquefiable,
normalized_blow_count,
lateral_displacement_potential,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_is\_t15\_liquefiable\_layers}(\mathrm{is\_potentially\_liquefiable}, N_{160}, LD_{potential}) \\ \hspace{1em} T_{15\ flag} \gets \mathrm{is\_potentially\_liquefiable} \mathbin{\&} \mathopen{}\left( N_{160} < 15 \mathclose{}\right) \mathbin{\&} LD_{potential} \\ \hspace{1em} \mathbf{return} \ T_{15\ flag} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
normalized_blow_count
|
float
|
N_60 corrected to 1 atm effective overburden stress |
required |
lateral_displacement_potential
|
bool
|
Applies when liquefiable group thickness >= min thickness |
required |
Returns:
| Name | Type | Description |
|---|---|---|
is_t15_liquefiable_layers |
bool
|
Liquefiable layers with N_160 < 15 |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_displacement\_inc\_\_idriss2008soil}(z) \\ \hspace{1em} LD_i \gets \mathrm{np}.\mathrm{full\_like} \mathopen{}\left( z, \mathrm{np}.\mathrm{nan} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LD_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
lateral_spread_displacement_inc |
float
|
Incremental lateral spread displacement |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_displacement\_index}(LDI_i) \\ \hspace{1em} LDI \gets \mathrm{reverse\_cumsum} \mathopen{}\left( LDI_i \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LDI \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
lateral_displacement_index_inc
|
float
|
Incremental lateral displacement index |
required |
Returns:
| Name | Type | Description |
|---|---|---|
lateral_displacement_index |
float
|
Lateral displacement index for liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_displacement\_index\_inc}(γ_{max}, H, LD_{potential}) \\ \hspace{1em} LDI_i \gets \frac{γ_{max}}{100} \cdot H \\ \hspace{1em} LDI_i \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( LD_{potential}, LDI_i, 0 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LDI_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
max_shear_strain
|
float
|
Maximum shear strain in soil |
required |
thickness
|
float
|
Thickness of soil layer |
required |
lateral_displacement_potential
|
bool
|
Applies when liquefiable group thickness >= min thickness |
required |
Returns:
| Name | Type | Description |
|---|---|---|
lateral_displacement_index_inc |
float
|
Incremental lateral displacement index |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_displacement\_index\_sum}(LDI_i) \\ \hspace{1em} ΣLDI \gets \sum LDI_i \\ \hspace{1em} \mathbf{return} \ ΣLDI \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
lateral_displacement_index_inc
|
float
|
Incremental lateral displacement index |
required |
Returns:
| Name | Type | Description |
|---|---|---|
lateral_displacement_index_sum |
float
|
Sum of lateral displacement indices |
get_lateral_displacement_potential(
is_potentially_liquefiable_thickness,
lateral_displacement_min_thickness,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_displacement\_potential}(\mathrm{is\_potentially\_liquefiable\_thickness}, LD_{min\ thickness}) \\ \hspace{1em} LD_{potential} \gets \mathrm{is\_potentially\_liquefiable\_thickness} \ge LD_{min\ thickness} \\ \hspace{1em} \mathbf{return} \ LD_{potential} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
is_potentially_liquefiable_thickness
|
float
|
Thickness of potentially liquefiable group |
required |
lateral_displacement_min_thickness
|
float
|
Minimum thickness for lateral displacement (Youd: 1.0 m, Zhang: 0.6 m) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
lateral_displacement_potential |
bool
|
Applies when liquefiable group thickness >= min thickness |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_spread\_displacement}(LD_i) \\ \hspace{1em} LD \gets \mathrm{reverse\_cumsum} \mathopen{}\left( LD_i \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LD \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
lateral_spread_displacement_inc
|
float
|
Incremental lateral spread displacement |
required |
Returns:
| Name | Type | Description |
|---|---|---|
lateral_spread_displacement |
float
|
Lateral spread displacement due to liquefaction |
get_lateral_spread_displacement_inc__youd2002revised(
site_ground_condition,
moment_magnitude,
site_to_seismic_source_distance,
lateral_displacement_potential,
is_t15_liquefiable_layers,
fines_content,
diameter_at_50_percent_finer,
thickness,
ground_slope=float("nan"),
free_face_height=float("nan"),
free_face_length=float("nan"),
lateral_spread_displacement_as_scalar=False,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_spread\_displacement\_inc\_\_youd2002revised}(\mathrm{site\_ground\_condition}, M_w, R, LD_{potential}, T_{15\ flag}, FC, D_{50}, H, S, H, L, LD_{scalar}) \\ \hspace{1em} LD_i \gets \mathrm{None} \\ \hspace{1em} \mathbf{if} \ \mathrm{site\_ground\_condition} = \textrm{"level\_ground"} \\ \hspace{2em} \mathbf{if} \ \lnot LD_{scalar} \\ \hspace{3em} LD_i \gets \mathrm{np}.\mathrm{zeros\_like} \mathopen{}\left( H \mathclose{}\right) \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} LD_i \gets 0 \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{2em} \mathbf{return} \ LD_i \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathopen{}\left( T_{15}, FC_{T15}, D_{50T15} \mathclose{}\right) \gets \mathrm{get\_youd2002revised\_t15\_parameters} \mathopen{}\left( T_{15\ flag}, FC, D_{50}, H, LD_{scalar} \mathclose{}\right) \\ \hspace{2em} \mathbf{if} \ \mathrm{site\_ground\_condition} = \textrm{"sloping\_ground"} \\ \hspace{3em} \mathbf{if} \ \lnot \mathopen{}\left( 0.1 \le S \le 6 \mathclose{}\right) \\ \hspace{4em} \mathrm{raise\_value\_error} \mathopen{}\left( \textrm{"ground\_slope must be between 0.1 to 6 \%"} \mathclose{}\right) \\ \hspace{3em} \mathbf{end \ if} \\ \hspace{3em} LD_i \gets 10^{-16.213 + 1.532 M_w - 1.406 \log_{10} \mathopen{}\left( 10^{0.89 M_w - 5.64} + R \mathclose{}\right) - 0.012 R + 0.338 \log_{10} S + 0.54 \log_{10} T_{15} + 3.413 \log_{10} \mathopen{}\left( 100.0 - FC_{T15} \mathclose{}\right) - 0.795 \log_{10} \mathopen{}\left( D_{50T15} + 0.1 \mathclose{}\right)} \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} \mathbf{if} \ \mathrm{site\_ground\_condition} = \textrm{"free\_face"} \\ \hspace{4em} \mathbf{if} \ \lnot \mathopen{}\left( 1 \le 100 \frac{H}{L} \le 20 \mathclose{}\right) \\ \hspace{5em} \mathrm{raise\_value\_error} \mathopen{}\left( \textrm{"free\_face\_height / free\_face\_length must be between 1 to 20 \%"} \mathclose{}\right) \\ \hspace{4em} \mathbf{end \ if} \\ \hspace{4em} LD_i \gets 10^{-16.713 + 1.532 M_w - 1.406 \log_{10} \mathopen{}\left( 10^{0.89 M_w - 5.64} + R \mathclose{}\right) - 0.012 R + 0.592 \log_{10} \mathopen{}\left( 100 \frac{H}{L} \mathclose{}\right) + 0.54 \log_{10} T_{15} + 3.413 \log_{10} \mathopen{}\left( 100 - FC_{T15} \mathclose{}\right) - 0.795 \log_{10} \mathopen{}\left( D_{50T15} + 0.1 \mathclose{}\right)} \\ \hspace{3em} \mathbf{end \ if} \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{2em} \mathbf{if} \ \lnot LD_{scalar} \\ \hspace{3em} LD_i \gets \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( LD_i \mathclose{}\right) \\ \hspace{3em} LD_i \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( LD_{potential}, LD_i, 0 \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ LD_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
site_ground_condition
|
str
|
Description of site ground condition |
required |
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
site_to_seismic_source_distance
|
float
|
Horizontal distance to nearest seismic energy source |
required |
lateral_displacement_potential
|
bool
|
Applies when liquefiable group thickness >= min thickness |
required |
is_t15_liquefiable_layers
|
bool
|
Liquefiable layers with N_160 < 15 |
required |
fines_content
|
float
|
Percentage of fines passing No. 200 sieve |
required |
diameter_at_50_percent_finer
|
float
|
Diameter at 50% finer from sieve analysis |
required |
thickness
|
float
|
Thickness of soil layer |
required |
ground_slope
|
float
|
Slope of ground surface |
float('nan')
|
free_face_height
|
float
|
Height of free face for lateral spreading analysis |
float('nan')
|
free_face_length
|
float
|
Distance from base of free face to point of interest |
float('nan')
|
lateral_spread_displacement_as_scalar
|
bool
|
If disabled, calculates lateral displacement for each depth |
False
|
Returns:
| Name | Type | Description |
|---|---|---|
lateral_spread_displacement_inc |
float
|
Incremental lateral spread displacement |
get_lateral_spread_displacement_inc__zhang2004estimating(
site_ground_condition,
lateral_displacement_index_inc,
ground_slope=float("nan"),
free_face_height=float("nan"),
free_face_length=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_spread\_displacement\_inc\_\_zhang2004estimating}(\mathrm{site\_ground\_condition}, LDI_i, S, H, L) \\ \hspace{1em} LD_{ratio} \gets \mathrm{None} \\ \hspace{1em} \mathbf{if} \ \mathrm{site\_ground\_condition} = \textrm{"level\_ground"} \\ \hspace{2em} LD_{ratio} \gets \mathrm{np}.\mathrm{zeros\_like} \mathopen{}\left( LDI_i \mathclose{}\right) \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ \mathrm{site\_ground\_condition} = \textrm{"sloping\_ground"} \\ \hspace{3em} \mathbf{if} \ \lnot \mathopen{}\left( 0.2 < S < 3.5 \mathclose{}\right) \\ \hspace{4em} \mathrm{raise\_value\_error} \mathopen{}\left( \textrm{"ground\_slope must be between 0.2 to 3.5 \%"} \mathclose{}\right) \\ \hspace{3em} \mathbf{end \ if} \\ \hspace{3em} LD_{ratio} \gets S + 0.2 \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} \mathbf{if} \ \mathrm{site\_ground\_condition} = \textrm{"free\_face"} \\ \hspace{4em} \mathbf{if} \ \lnot \mathopen{}\left( 4 < \frac{L}{H} < 40 \mathclose{}\right) \\ \hspace{5em} \mathrm{raise\_value\_error} \mathopen{}\left( \textrm{"free\_face\_height / free\_face\_length must be between 4 to 40"} \mathclose{}\right) \\ \hspace{4em} \mathbf{end \ if} \\ \hspace{4em} LD_{ratio} \gets 6 \mathopen{}\left( \frac{L}{H} \mathclose{}\right)^{-0.8} \\ \hspace{3em} \mathbf{end \ if} \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} LD_i \gets LDI_i \cdot LD_{ratio} \\ \hspace{1em} \mathbf{return} \ LD_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
site_ground_condition
|
str
|
Description of site ground condition |
required |
lateral_displacement_index_inc
|
float
|
Incremental lateral displacement index |
required |
ground_slope
|
float
|
Slope of ground surface |
float('nan')
|
free_face_height
|
float
|
Height of free face for lateral spreading analysis |
float('nan')
|
free_face_length
|
float
|
Distance from base of free face to point of interest |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
lateral_spread_displacement_inc |
float
|
Incremental lateral spread displacement |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_lateral\_spread\_displacement\_sum}(LD_i) \\ \hspace{1em} ΣLD \gets \sum LD_i \\ \hspace{1em} \mathbf{return} \ ΣLD \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
lateral_spread_displacement_inc
|
float
|
Incremental lateral spread displacement |
required |
Returns:
| Name | Type | Description |
|---|---|---|
lateral_spread_displacement_sum |
float
|
Sum of lateral spread displacements |
get_liquefaction_building_settlement_index__bray2017simplified(
footing_embedment, max_shear_strain, depth, thickness
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_building\_settlement\_index\_\_bray2017simplified}(D_f, γ_{max}, z, H) \\ \hspace{1em} z_{middle} \gets \mathrm{get\_depth\_middle} \mathopen{}\left( z, H \mathclose{}\right) \\ \hspace{1em} W \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( z < D_f, 0, 1 \mathclose{}\right) \\ \hspace{1em} LBS \gets \sum \mathopen{}\left( W \frac{γ_{max}}{z_{middle}} \cdot H \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LBS \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
footing_embedment
|
float
|
Depth of footing embedment |
required |
max_shear_strain
|
float
|
Maximum shear strain in soil |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
thickness
|
float
|
Thickness of soil layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_building_settlement_index |
float
|
Liquefaction-induced building settlement index |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_potential\_index}(LPI_i) \\ \hspace{1em} LPI \gets \mathrm{reverse\_cumsum} \mathopen{}\left( LPI_i \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LPI \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_potential_index_inc
|
float
|
Incremental liquefaction potential index |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_potential_index |
float
|
Liquefaction potential index for site |
get_liquefaction_potential_index_inc(
liquefaction_safety_factor,
depth,
thickness,
liquefaction_potential_index_method,
thickness_non_liquefiable_layer=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_potential\_index\_inc}(FS_{liq}, z, H, ΣLPI_{method}, H_1) \\ \hspace{1em} LPI_i \gets \mathrm{None} \\ \hspace{1em} \mathbf{if} \ ΣLPI_{method} = \textrm{"iwasaki1978"} \\ \hspace{2em} LPI_i \gets \mathrm{get\_liquefaction\_potential\_index\_inc\_\_iwasaki1978practical} \mathopen{}\left( FS_{liq}, z, H \mathclose{}\right) \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathbf{if} \ ΣLPI_{method} = \textrm{"maurer2015"} \\ \hspace{3em} LPI_i \gets \mathrm{get\_liquefaction\_potential\_index\_inc\_\_maurer2015moving} \mathopen{}\left( FS_{liq}, z, H, H_1 \mathclose{}\right) \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ LPI_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
thickness
|
float
|
Thickness of soil layer |
required |
liquefaction_potential_index_method
|
str
|
Liquefaction potential index method |
required |
thickness_non_liquefiable_layer
|
float
|
Thickness of non-liquefiable surface layer |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_potential_index_inc |
float
|
Incremental liquefaction potential index |
get_liquefaction_potential_index_inc__iwasaki1978practical(
liquefaction_safety_factor, depth, thickness
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_potential\_index\_inc\_\_iwasaki1978practical}(FS_{liq}, z, H) \\ \hspace{1em} LPI_i \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( FS_{liq} \le 1, 1 - FS_{liq}, 0 \mathclose{}\right) \cdot \mathrm{np}.\mathrm{where} \mathopen{}\left( z \le 20, 10 - 0.5 z, 0 \mathclose{}\right) H \\ \hspace{1em} LPI_i \gets \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( LPI_i \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LPI_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
thickness
|
float
|
Thickness of soil layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_potential_index_inc |
float
|
Incremental liquefaction potential index |
get_liquefaction_potential_index_inc__maurer2015moving(
liquefaction_safety_factor,
depth,
thickness,
thickness_non_liquefiable_layer,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_potential\_index\_inc\_\_maurer2015moving}(FS_{liq}, z, H, H_1) \\ \hspace{1em} \mathrm{m\_i} \gets \exp \mathopen{}\left( \frac{5}{25.56 \mathopen{}\left( 1 - FS_{liq} \mathclose{}\right)} \mathclose{}\right) - 1 \\ \hspace{1em} H_1 \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( H_1, 0.4, \mathrm{None} \mathclose{}\right) \\ \hspace{1em} LPI_i \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathopen{}\left( FS_{liq} \le 1 \mathclose{}\right) \mathbin{\&} \mathopen{}\left( H_1 \cdot \mathrm{m\_i} \le 3 \mathclose{}\right), 1 - FS_{liq}, 0 \mathclose{}\right) \cdot \mathrm{np}.\mathrm{where} \mathopen{}\left( z \le 20, \frac{25.56}{z}, 0 \mathclose{}\right) H \\ \hspace{1em} LPI_i \gets \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( LPI_i \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LPI_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
thickness
|
float
|
Thickness of soil layer |
required |
thickness_non_liquefiable_layer
|
float
|
Thickness of non-liquefiable surface layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_potential_index_inc |
float
|
Incremental liquefaction potential index |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_potential\_index\_sum}(LPI_i) \\ \hspace{1em} ΣLPI \gets \sum LPI_i \\ \hspace{1em} \mathbf{return} \ ΣLPI \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_potential_index_inc
|
float
|
Incremental liquefaction potential index |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_potential_index_sum |
float
|
Sum of liquefaction potential indices |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_potential\_index\_sum\_label}(ΣLPI) \\ \hspace{1em} ΣLPI_{label} \gets \mathrm{parameter\_registry}.\mathrm{bin\_data} \mathopen{}\left( \textrm{"liquefaction\_potential\_index\_sum"}, ΣLPI, \textrm{"liquefaction\_potential\_index\_sum\_label"} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ ΣLPI_{label} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_potential_index_sum
|
float
|
Sum of liquefaction potential indices |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_potential_index_sum_label |
str
|
Label for sum of liquefaction potential indices |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_probability\_\_boulanger2014cpt}(FS_{liq}) \\ \hspace{1em} PL_{liq} \gets 100 \mathopen{}\left( 1 - \mathrm{norm} \mathopen{}\left( \mathclose{}\right).\mathrm{cdf} \mathopen{}\left( \frac{0.2 + \log FS_{liq}}{0.2} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} PL_{liq} \gets \mathrm{np}.\mathrm{asarray} \mathopen{}\left( PL_{liq} \mathclose{}\right) \\ \hspace{1em} \mathrm{np}.\mathrm{putmask} \mathopen{}\left( PL_{liq}, FS_{liq} \ge 2, 0 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ PL_{liq} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_probability |
float
|
Probability of liquefaction occurrence |
get_liquefaction_probability__cetin2004standard(
normalized_blow_count,
effective_stress,
fines_content,
moment_magnitude,
cyclic_stress_ratio,
is_potentially_liquefiable,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_probability\_\_cetin2004standard}(N_{160}, σ_v', FC, M_w, CSR, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} \mathopen{}\left( \mathrm{theta1}, \mathrm{theta2}, \mathrm{theta3}, \mathrm{theta4}, \mathrm{theta5}, \mathrm{theta6}, \mathrm{sigma\_epsilon} \mathclose{}\right) \gets \mathrm{list} \mathopen{}\left( \mathrm{ReferenceDataSets}.\mathrm{ModelCoefficientsCetin}.\mathrm{to\_index\_map} \mathopen{}\left( \textrm{"theta"}, \textrm{"2004"} \mathclose{}\right).\mathrm{values} \mathopen{}\left( \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} FC \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( FC, 5, 35 \mathclose{}\right) \\ \hspace{1em} PL_{liq} \gets 100 \mathrm{norm} \mathopen{}\left( \mathclose{}\right).\mathrm{cdf} \mathopen{}\left( \frac{-\mathopen{}\left( N_{160} \cdot \mathopen{}\left( 1 + \mathrm{theta1} \cdot FC \mathclose{}\right) - \mathrm{theta6} \cdot \log CSR - \mathrm{theta2} \cdot \log M_w - \mathrm{theta3} \cdot \log \mathopen{}\left( \frac{σ_v'}{101.325} \mathclose{}\right) + \mathrm{theta4} \cdot FC + \mathrm{theta5} \mathclose{}\right)}{\mathrm{sigma\_epsilon}} \mathclose{}\right) \\ \hspace{1em} PL_{liq} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathrm{np}.\mathrm{isnan} \mathopen{}\left( PL_{liq} \mathclose{}\right) \mathbin{|} \mathord{\sim} \mathrm{is\_potentially\_liquefiable}, 0, PL_{liq} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ PL_{liq} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
normalized_blow_count
|
float
|
N_60 corrected to 1 atm effective overburden stress |
required |
effective_stress
|
float
|
Effective vertical stress in soil |
required |
fines_content
|
float
|
Percentage of fines passing No. 200 sieve |
required |
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
cyclic_stress_ratio
|
float
|
Cyclic stress ratio for liquefaction |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_probability |
float
|
Probability of liquefaction occurrence |
get_liquefaction_probability__cetin2018use(
normalized_blow_count,
effective_stress,
fines_content,
moment_magnitude,
cyclic_stress_ratio,
is_potentially_liquefiable,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_probability\_\_cetin2018use}(N_{160}, σ_v', FC, M_w, CSR, \mathrm{is\_potentially\_liquefiable}) \\ \hspace{1em} \mathopen{}\left( \mathrm{theta1}, \mathrm{theta2}, \mathrm{theta3}, \mathrm{theta4}, \mathrm{theta5}, \mathrm{theta6}, \mathrm{sigma\_epsilon} \mathclose{}\right) \gets \mathrm{list} \mathopen{}\left( \mathrm{ReferenceDataSets}.\mathrm{ModelCoefficientsCetin}.\mathrm{to\_index\_map} \mathopen{}\left( \textrm{"theta"}, \textrm{"2018"} \mathclose{}\right).\mathrm{values} \mathopen{}\left( \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} FC \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( FC, 5, 35 \mathclose{}\right) \\ \hspace{1em} PL_{liq} \gets 100 \mathrm{norm} \mathopen{}\left( \mathclose{}\right).\mathrm{cdf} \mathopen{}\left( \frac{-\mathopen{}\left( N_{160} \cdot \mathopen{}\left( 1 + \mathrm{theta1} \cdot FC \mathclose{}\right) - \mathrm{theta6} \cdot \log CSR - \mathrm{theta2} \cdot \log M_w - \mathrm{theta3} \cdot \log \mathopen{}\left( \frac{σ_v'}{101.325} \mathclose{}\right) + \mathrm{theta4} \cdot FC + \mathrm{theta5} \mathclose{}\right)}{\mathrm{sigma\_epsilon}} \mathclose{}\right) \\ \hspace{1em} PL_{liq} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathrm{np}.\mathrm{isnan} \mathopen{}\left( PL_{liq} \mathclose{}\right) \mathbin{|} \mathord{\sim} \mathrm{is\_potentially\_liquefiable}, 0, PL_{liq} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ PL_{liq} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
normalized_blow_count
|
float
|
N_60 corrected to 1 atm effective overburden stress |
required |
effective_stress
|
float
|
Effective vertical stress in soil |
required |
fines_content
|
float
|
Percentage of fines passing No. 200 sieve |
required |
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
cyclic_stress_ratio
|
float
|
Cyclic stress ratio for liquefaction |
required |
is_potentially_liquefiable
|
bool
|
Indicates if soil is potentially liquefiable |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_probability |
float
|
Probability of liquefaction occurrence |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_probability\_\_idriss2008soil}(FS_{liq}) \\ \hspace{1em} PL_{liq} \gets 100 \mathopen{}\left( 1 - \mathrm{norm} \mathopen{}\left( \mathclose{}\right).\mathrm{cdf} \mathopen{}\left( \frac{0 + \log FS_{liq}}{0.13} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} PL_{liq} \gets \mathrm{np}.\mathrm{asarray} \mathopen{}\left( PL_{liq} \mathclose{}\right) \\ \hspace{1em} \mathrm{np}.\mathrm{putmask} \mathopen{}\left( PL_{liq}, FS_{liq} \ge 2, 0 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ PL_{liq} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_probability |
float
|
Probability of liquefaction occurrence |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_probability\_\_ku2012probabilistic}(FS_{liq}) \\ \hspace{1em} PL_{liq} \gets 100 \mathopen{}\left( 1 - \mathrm{norm} \mathopen{}\left( \mathclose{}\right).\mathrm{cdf} \mathopen{}\left( \frac{0.102 + \log FS_{liq}}{0.276} \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ PL_{liq} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_probability |
float
|
Probability of liquefaction occurrence |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_safety\_factor}(CRR, CSR) \\ \hspace{1em} FS_{liq} \gets \frac{CRR}{CSR} \\ \hspace{1em} FS_{liq} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( FS_{liq}, \mathrm{None}, 2 \mathclose{}\right) \\ \hspace{1em} FS_{liq} \gets \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( FS_{liq} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ FS_{liq} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
cyclic_resistance_ratio
|
float
|
Cyclic resistance ratio for liquefaction |
required |
cyclic_stress_ratio
|
float
|
Cyclic stress ratio for liquefaction |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_safety_factor |
float
|
Factor of safety against liquefaction triggering |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_settlement}(S_{v-1D\ i}) \\ \hspace{1em} S_{v-1D} \gets \mathrm{reverse\_cumsum} \mathopen{}\left( S_{v-1D\ i} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ S_{v-1D} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_settlement_inc
|
float
|
Incremental post-liquefaction vertical settlement |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_settlement |
float
|
Post-liquefaction vertical unidimensional settlement |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_settlement\_inc}(ε_v, H) \\ \hspace{1em} S_{v-1D\ i} \gets \frac{ε_v}{100} \cdot H \\ \hspace{1em} \mathbf{return} \ S_{v-1D\ i} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
volumetric_strain
|
float
|
Volumetric strain in soil |
required |
thickness
|
float
|
Thickness of soil layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_settlement_inc |
float
|
Incremental post-liquefaction vertical settlement |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_settlement\_sum}(S_{v-1D\ i}) \\ \hspace{1em} ΣS_{v-1D} \gets \sum S_{v-1D\ i} \\ \hspace{1em} \mathbf{return} \ ΣS_{v-1D} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_settlement_inc
|
float
|
Incremental post-liquefaction vertical settlement |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_settlement_sum |
float
|
Sum of post-liquefaction vertical settlements |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_severity\_number}(LSN_i) \\ \hspace{1em} LSN \gets \mathrm{reverse\_cumsum} \mathopen{}\left( LSN_i \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LSN \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_severity_number_inc
|
float
|
Incremental liquefaction severity number |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_severity_number |
float
|
Liquefaction severity number for site |
get_liquefaction_severity_number_inc__van2014assessment(
volumetric_strain,
depth,
thickness,
liquefaction_severity_number_max_depth,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_severity\_number\_inc\_\_van2014assessment}(ε_v, z, H, LSN_{max\ z}) \\ \hspace{1em} LSN_i \gets 1000 \frac{\frac{ε_v}{100}}{z} \cdot H \\ \hspace{1em} LSN_i \gets \mathrm{np}.\mathrm{asarray} \mathopen{}\left( LSN_i \mathclose{}\right) \\ \hspace{1em} \mathrm{flag} \gets z > LSN_{max\ z} \\ \hspace{1em} \mathrm{flag} \gets \mathrm{np}.\mathrm{broadcast\_to} \mathopen{}\left( \mathrm{flag}, LSN_i.\mathrm{shape} \mathclose{}\right) \\ \hspace{1em} \mathrm{np}.\mathrm{putmask} \mathopen{}\left( LSN_i, \mathrm{flag}, \mathrm{np}.\mathrm{nan} \mathclose{}\right) \\ \hspace{1em} LSN_i \gets \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( LSN_i \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ LSN_i \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
volumetric_strain
|
float
|
Volumetric strain in soil |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
thickness
|
float
|
Thickness of soil layer |
required |
liquefaction_severity_number_max_depth
|
float
|
Maximum depth for liquefaction severity number analysis |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_severity_number_inc |
float
|
Incremental liquefaction severity number |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_severity\_number\_sum}(LSN_i) \\ \hspace{1em} ΣLSN \gets \sum LSN_i \\ \hspace{1em} \mathbf{return} \ ΣLSN \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_severity_number_inc
|
float
|
Incremental liquefaction severity number |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_severity_number_sum |
float
|
Sum of liquefaction severity numbers |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_severity\_number\_sum\_label}(ΣLSN) \\ \hspace{1em} ΣLSN_{label} \gets \mathrm{parameter\_registry}.\mathrm{bin\_data} \mathopen{}\left( \textrm{"liquefaction\_severity\_number\_sum"}, ΣLSN, \textrm{"liquefaction\_severity\_number\_sum\_label"} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ ΣLSN_{label} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_severity_number_sum
|
float
|
Sum of liquefaction severity numbers |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_severity_number_sum_label |
str
|
Label for sum of liquefaction severity numbers |
get_liquefaction_shear_induced_building_settlement__bray2017simplified(
footing_width,
thickness_liquefiable_layer,
liquefaction_building_settlement_index,
standardized_cumulative_absolute_velocity,
spectral_acceleration_at_1_sec,
foundation_contact_pressure,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_shear\_induced\_building\_settlement\_\_bray2017simplified}(B, H_2, LBS, CAV_{STD}, Sa_1, Q) \\ \hspace{1em} \epsilon \gets 0 \\ \hspace{1em} \mathbf{if} \ LBS \le 16 \\ \hspace{2em} \mathrm{c1} \gets -8.35 \\ \hspace{2em} \mathrm{c2} \gets 0.072 \\ \hspace{1em} \mathbf{else} \\ \hspace{2em} \mathrm{c1} \gets -7.48 \\ \hspace{2em} \mathrm{c2} \gets 0.014 \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} D_s \gets \exp \mathopen{}\left( \mathrm{c1} + 4.59 \log Q - 0.42 \mathopen{}\left( \log Q \mathclose{}\right)^{2} + \mathrm{c2} \cdot LBS + 0.58 \log \tanh \mathopen{}\left( \frac{H_2}{6} \mathclose{}\right) - 0.02 B + 0.84 \log CAV_{STD} + 0.41 \log Sa_1 + \epsilon \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ D_s \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
footing_width
|
float
|
Footing width (small plan dimension) |
required |
thickness_liquefiable_layer
|
float
|
Thickness of liquefiable sand layer |
required |
liquefaction_building_settlement_index
|
float
|
Liquefaction-induced building settlement index |
required |
standardized_cumulative_absolute_velocity
|
float
|
Standardized cumulative absolute velocity |
required |
spectral_acceleration_at_1_sec
|
float
|
Spectral acceleration at 1-second period |
required |
foundation_contact_pressure
|
float
|
Contact pressure of building's foundation |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_shear_induced_building_settlement |
float
|
Shear-induced building settlement due to liquefaction |
get_liquefaction_susceptibility__bray2006assessment(
water_content_liquid_limit_ratio, plasticity_index
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_liquefaction\_susceptibility\_\_bray2006assessment}(w_c\ /\ LL, PI) \\ \hspace{1em} \mathrm{liquefaction\_susceptibility} \gets \mathrm{ReferenceFigureRegistry}.\mathrm{LiquefactionSusceptibility}.\mathrm{assign\_polygons\_labels\_from\_xy\_data} \mathopen{}\left( w_c\ /\ LL, PI \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ \mathrm{liquefaction\_susceptibility} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
water_content_liquid_limit_ratio
|
float
|
Ratio of water content to liquid limit |
required |
plasticity_index
|
float
|
Plasticity index of soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
liquefaction_susceptibility |
str
|
Susceptibility of soil to liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_magnitude\_scaling\_factor\_\_boulanger2014cpt}(M_w, MSF_{max}) \\ \hspace{1em} MSF \gets 1 + \mathopen{}\left( MSF_{max} - 1 \mathclose{}\right) \mathopen{}\left( 8.64 \exp \mathopen{}\left( \frac{-M_w}{4} \mathclose{}\right) - 1.325 \mathclose{}\right) \\ \hspace{1em} MSF \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( MSF, \mathrm{None}, MSF_{max} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ MSF \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
magnitude_scaling_factor_max
|
float
|
Maximum magnitude scaling factor |
required |
Returns:
| Name | Type | Description |
|---|---|---|
magnitude_scaling_factor |
float
|
Magnitude scaling factor for liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_magnitude\_scaling\_factor\_\_cetin2018use}(M_w) \\ \hspace{1em} \mathrm{cetineayy\_coeffs} \gets \mathrm{ReferenceDataSets}.\mathrm{ModelCoefficientsCetin}.\mathrm{to\_index\_map} \mathopen{}\left( \textrm{"theta"}, \textrm{"2018"} \mathclose{}\right) \\ \hspace{1em} \mathopen{}\left( \mathrm{theta2}, \mathrm{theta6} \mathclose{}\right) \gets \mathopen{}\left( \mathrm{cetineayy\_coeffs}_{\textrm{"2"}}, \mathrm{cetineayy\_coeffs}_{\textrm{"6"}} \mathclose{}\right) \\ \hspace{1em} M_w \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( M_w, 5.5, 8.4 \mathclose{}\right) \\ \hspace{1em} MSF \gets \mathopen{}\left( \frac{M_w}{7.5} \mathclose{}\right)^{\frac{-\mathrm{theta2}}{\mathrm{theta6}}} \\ \hspace{1em} \mathbf{return} \ MSF \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
Returns:
| Name | Type | Description |
|---|---|---|
magnitude_scaling_factor |
float
|
Magnitude scaling factor for liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_magnitude\_scaling\_factor\_\_idriss2008soil}(M_w) \\ \hspace{1em} MSF \gets 6.9 \exp \mathopen{}\left( \frac{-M_w}{4} \mathclose{}\right) - 0.058 \\ \hspace{1em} MSF \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( MSF, \mathrm{None}, 1.8 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ MSF \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
Returns:
| Name | Type | Description |
|---|---|---|
magnitude_scaling_factor |
float
|
Magnitude scaling factor for liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_magnitude\_scaling\_factor\_\_youd2001liquefaction}(M_w) \\ \hspace{1em} MSF \gets \frac{10^{2.24}}{M_w^{2.56}} \\ \hspace{1em} \mathbf{return} \ MSF \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
Returns:
| Name | Type | Description |
|---|---|---|
magnitude_scaling_factor |
float
|
Magnitude scaling factor for liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_magnitude\_scaling\_factor\_max\_spt\_\_boulanger2014cpt}(N_{160cs}) \\ \hspace{1em} MSF_{max} \gets 1.09 + \mathopen{}\left( \frac{N_{160cs}}{31.5} \mathclose{}\right)^{2} \\ \hspace{1em} MSF_{max} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( MSF_{max}, \mathrm{None}, 2.2 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ MSF_{max} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
clean_sand_normalized_blow_count
|
float
|
Equivalent clean sand SPT blow count (N_160) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
magnitude_scaling_factor_max |
float
|
Maximum magnitude scaling factor |
get_max_shear_strain__cetin2009probabilistica(
clean_sand_normalized_blow_count,
liquefaction_safety_factor,
cyclic_stress_ratio_ss_20_1d_1atm,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_max\_shear\_strain\_\_cetin2009probabilistica}(N_{160cs}, FS_{liq}, CSR_{SS,20,1D,1atm}) \\ \hspace{1em} CSR_{SS,20,1D,1atm} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( CSR_{SS,20,1D,1atm}, 0.05, 0.6 \mathclose{}\right) \\ \hspace{1em} N_{160cs} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( N_{160cs}, 5, 40 \mathclose{}\right) \\ \hspace{1em} γ_{max} \gets \frac{-0.025 N_{160cs} + \log CSR_{SS,20,1D,1atm} + 2.613}{0.004 N_{160cs} + 0.001} \\ \hspace{1em} γ_{max} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( \mathrm{np}.\mathrm{isnan} \mathopen{}\left( γ_{max} \mathclose{}\right) \mathbin{|} \mathopen{}\left( FS_{liq} \ge 2 \mathclose{}\right), 0, \mathrm{np}.\mathrm{clip} \mathopen{}\left( γ_{max}, 0, 100 \mathclose{}\right) \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ γ_{max} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
clean_sand_normalized_blow_count
|
float
|
Equivalent clean sand SPT blow count (N_160) |
required |
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
cyclic_stress_ratio_ss_20_1d_1atm
|
float
|
CSR value corresponding to a 1 dimensional, 20 uniform loading cycles simple shear test under a confinement pressure of 1 atm |
required |
Returns:
| Name | Type | Description |
|---|---|---|
max_shear_strain |
float
|
Maximum shear strain in soil |
get_max_shear_strain__idriss2008soil(
liquefaction_safety_factor,
max_shear_strain_f_alpha_term,
shear_strain_limit,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_max\_shear\_strain\_\_idriss2008soil}(FS_{liq}, F_α, γ_{lim}) \\ \hspace{1em} \mathrm{condition\_1} \gets FS_{liq} \ge 2 \\ \hspace{1em} \mathrm{choice\_1} \gets 0.0 \\ \hspace{1em} \mathrm{condition\_2} \gets \mathopen{}\left( FS_{liq} > F_α \mathclose{}\right) \mathbin{\&} \mathopen{}\left( FS_{liq} < 2 \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_2} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( \frac{100 \cdot 0.035 \mathopen{}\left( 1 - F_α \mathclose{}\right) \mathopen{}\left( 2 - FS_{liq} \mathclose{}\right)}{FS_{liq} - F_α}, \mathrm{None}, γ_{lim} \mathclose{}\right) \\ \hspace{1em} \mathrm{condition\_3} \gets FS_{liq} \le F_α \\ \hspace{1em} \mathrm{choice\_3} \gets γ_{lim} \\ \hspace{1em} γ_{max} \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2}, \mathrm{condition\_3} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2}, \mathrm{choice\_3} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ γ_{max} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
max_shear_strain_f_alpha_term
|
float
|
Term for maximum shear strain calculation |
required |
shear_strain_limit
|
float
|
Limiting value of shear strain |
required |
Returns:
| Name | Type | Description |
|---|---|---|
max_shear_strain |
float
|
Maximum shear strain in soil |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_max\_shear\_strain\_f\_alpha\_term\_spt\_\_idriss2008soil}(N_{160cs}) \\ \hspace{1em} N_{160cs} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( N_{160cs}, 7, \mathrm{None} \mathclose{}\right) \\ \hspace{1em} F_α \gets 0.032 + 0.69 \sqrt{ N_{160cs} } - 0.13 N_{160cs} \\ \hspace{1em} F_α \gets \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( F_α \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ F_α \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
clean_sand_normalized_blow_count
|
float
|
Equivalent clean sand SPT blow count (N_160) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
max_shear_strain_f_alpha_term |
float
|
Term for maximum shear strain calculation |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_membrane\_compliance\_correction\_\_cetin2009probabilistica}(D_r) \\ \hspace{1em} K_{mc} \gets -3e-05 D_r^{2} + 0.0048 D_r + 0.7222 \\ \hspace{1em} \mathbf{return} \ K_{mc} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
relative_density
|
float
|
Relative density of soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
membrane_compliance_correction |
float
|
Correction factor for membrane compliance in DMT |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_overburden\_correction\_coefficient\_spt\_\_idriss2006semi}(N_{160}) \\ \hspace{1em} N_{160} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( N_{160}, \mathrm{None}, 37 \mathclose{}\right) \\ \hspace{1em} C_σ \gets \frac{1}{18.9 - 2.55 \sqrt{ N_{160} }} \\ \hspace{1em} \mathbf{return} \ C_σ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
normalized_blow_count
|
float
|
N_60 corrected to 1 atm effective overburden stress |
required |
Returns:
| Name | Type | Description |
|---|---|---|
overburden_correction_coefficient |
float
|
Coefficient for overburden correction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_overburden\_correction\_coefficient\_spt\_\_idriss2008soil}(N_{160cs}) \\ \hspace{1em} \mathbf{return} \ \mathrm{get\_overburden\_correction\_coefficient\_spt\_\_idriss2006semi} \mathopen{}\left( N_{160cs} \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
clean_sand_normalized_blow_count
|
float
|
Equivalent clean sand SPT blow count (N_160) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
overburden_correction_coefficient |
float
|
Coefficient for overburden correction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_overburden\_correction\_crr\_\_cetin2018use}(σ_v') \\ \hspace{1em} \mathrm{cetineayy\_coeffs} \gets \mathrm{ReferenceDataSets}.\mathrm{ModelCoefficientsCetin}.\mathrm{to\_index\_map} \mathopen{}\left( \textrm{"theta"}, \textrm{"2018"} \mathclose{}\right) \\ \hspace{1em} \mathopen{}\left( \mathrm{theta3}, \mathrm{theta6} \mathclose{}\right) \gets \mathopen{}\left( \mathrm{cetineayy\_coeffs}_{\textrm{"3"}}, \mathrm{cetineayy\_coeffs}_{\textrm{"6"}} \mathclose{}\right) \\ \hspace{1em} K_σ \gets \mathopen{}\left( \frac{σ_v'}{101.325} \mathclose{}\right)^{\frac{-\mathrm{theta3}}{\mathrm{theta6}}} \\ \hspace{1em} K_σ \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( K_σ, 0.8, 1.6 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ K_σ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
effective_stress
|
float
|
Effective vertical stress in soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
overburden_correction_crr |
float
|
Overburden correction factor for cyclic resistance ratio |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_overburden\_correction\_crr\_\_hynes2018influence}(σ_v') \\ \hspace{1em} f \gets 0.8 \\ \hspace{1em} K_σ \gets \mathopen{}\left( \frac{σ_v'}{101.325} \mathclose{}\right)^{f - 1} \\ \hspace{1em} K_σ \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( K_σ, 0, 1 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ K_σ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
effective_stress
|
float
|
Effective vertical stress in soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
overburden_correction_crr |
float
|
Overburden correction factor for cyclic resistance ratio |
get_overburden_correction_crr__idriss2006semi(
overburden_correction_coefficient, effective_stress
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_overburden\_correction\_crr\_\_idriss2006semi}(C_σ, σ_v') \\ \hspace{1em} K_σ \gets 1 - C_σ \cdot \log \mathopen{}\left( \frac{σ_v'}{101.325} \mathclose{}\right) \\ \hspace{1em} K_σ \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( K_σ, \mathrm{None}, 1.1 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ K_σ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
overburden_correction_coefficient
|
float
|
Coefficient for overburden correction |
required |
effective_stress
|
float
|
Effective vertical stress in soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
overburden_correction_crr |
float
|
Overburden correction factor for cyclic resistance ratio |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_overburden\_correction\_crr\_\_youd2001liquefaction}(D_r, σ_v') \\ \hspace{1em} K_σ \gets \mathopen{}\left( \frac{σ_v'}{101.325} \mathclose{}\right)^{1 - 0.005 \frac{D_r}{100} - 1} \\ \hspace{1em} \mathbf{return} \ K_σ \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
relative_density
|
float
|
Relative density of soil |
required |
effective_stress
|
float
|
Effective vertical stress in soil |
required |
Returns:
| Name | Type | Description |
|---|---|---|
overburden_correction_crr |
float
|
Overburden correction factor for cyclic resistance ratio |
get_post_liquefaction_residual_shear_strength(
normalized_residual_shear_strength,
effective_stress,
is_fine_soil,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_post\_liquefaction\_residual\_shear\_strength}(S_{r\ ratio}, σ_v', \mathrm{is\_fine\_soil}) \\ \hspace{1em} S_r \gets S_{r\ ratio} \cdot σ_v' \\ \hspace{1em} S_r \gets \mathrm{np}.\mathrm{asarray} \mathopen{}\left( S_r \mathclose{}\right) \\ \hspace{1em} \mathrm{np}.\mathrm{putmask} \mathopen{}\left( S_r, \mathrm{is\_fine\_soil}, \mathrm{np}.\mathrm{nan} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ S_r \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
normalized_residual_shear_strength
|
float
|
Post-liquefaction residual shear strength to effective stress ratio |
required |
effective_stress
|
float
|
Effective vertical stress in soil |
required |
is_fine_soil
|
bool
|
Indicates if soil is fine-grained |
required |
Returns:
| Name | Type | Description |
|---|---|---|
post_liquefaction_residual_shear_strength |
float
|
Post-liquefaction residual shear strength |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_shear\_strain\_limit\_spt\_\_idriss2008soil}(N_{160cs}) \\ \hspace{1em} γ_{lim} \gets 100 \cdot 1.859 \mathopen{}\left( 1.1 - \sqrt{ \frac{N_{160cs}}{46} } \mathclose{}\right)^{3} \\ \hspace{1em} γ_{lim} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( γ_{lim}, 0, 50 \mathclose{}\right) \\ \hspace{1em} γ_{lim} \gets \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( γ_{lim} \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ γ_{lim} \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
clean_sand_normalized_blow_count
|
float
|
Equivalent clean sand SPT blow count (N_160) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
shear_strain_limit |
float
|
Limiting value of shear strain |
get_shear_stress_reduction_coefficient__cetin2004standard(
depth,
moment_magnitude,
peak_ground_acceleration,
average_shear_velocity_12m,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_shear\_stress\_reduction\_coefficient\_\_cetin2004standard}(z, M_w, PGA, V_{s12}) \\ \hspace{1em} r_d \gets \frac{1 + \frac{-23.013 - 2.949 PGA + 0.999 M_w + 0.0525 V_{s12}}{16.258 + 0.201 \exp \mathopen{}\left( 0.341 \mathopen{}\left( -z + 0.0785 V_{s12} + 7.586 \mathclose{}\right) \mathclose{}\right)}}{1 + \frac{-23.013 - 2.949 PGA + 0.999 M_w + 0.0525 V_{s12}}{16.258 + 0.201 \exp \mathopen{}\left( 0.341 \mathopen{}\left( 0.0785 V_{s12} + 7.586 \mathclose{}\right) \mathclose{}\right)}} - 0.0046 \mathopen{}\left( \mathrm{np}.\mathrm{clip} \mathopen{}\left( z, 20, \mathrm{None} \mathclose{}\right) - 20 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ r_d \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
peak_ground_acceleration
|
float
|
Peak ground acceleration for seismic analysis |
required |
average_shear_velocity_12m
|
float
|
Average shear wave velocity to 12 m depth |
required |
Returns:
| Name | Type | Description |
|---|---|---|
shear_stress_reduction_coefficient |
float
|
Shear stress reduction coefficient for liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_shear\_stress\_reduction\_coefficient\_\_idriss2006semi}(z, M_w) \\ \hspace{1em} \alpha \gets -1.012 - 1.126 \sin \mathopen{}\left( \frac{z}{11.73} + 5.133 \mathclose{}\right) \\ \hspace{1em} \beta \gets 0.106 + 0.118 \sin \mathopen{}\left( \frac{z}{11.28} + 5.142 \mathclose{}\right) \\ \hspace{1em} r_d \gets \exp \mathopen{}\left( \alpha + M_w \cdot \beta \mathclose{}\right) \\ \hspace{1em} r_d \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( r_d, \mathrm{None}, 1 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ r_d \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
moment_magnitude
|
float
|
Seismic moment magnitude |
required |
Returns:
| Name | Type | Description |
|---|---|---|
shear_stress_reduction_coefficient |
float
|
Shear stress reduction coefficient for liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_shear\_stress\_reduction\_coefficient\_\_liao1986catalog}(z) \\ \hspace{1em} \mathrm{condition\_1} \gets z \le 9.15 \\ \hspace{1em} \mathrm{choice\_1} \gets 1 - 0.00765 z \\ \hspace{1em} \mathrm{condition\_2} \gets \mathopen{}\left( z > 9.15 \mathclose{}\right) \mathbin{\&} \mathopen{}\left( z \le 23 \mathclose{}\right) \\ \hspace{1em} \mathrm{choice\_2} \gets 1.174 - 0.0267 z \\ \hspace{1em} r_d \gets \mathrm{np}.\mathrm{select} \mathopen{}\left( \mathopen{}\left[ \mathrm{condition\_1}, \mathrm{condition\_2} \mathclose{}\right], \mathopen{}\left[ \mathrm{choice\_1}, \mathrm{choice\_2} \mathclose{}\right] \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ r_d \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
shear_stress_reduction_coefficient |
float
|
Shear stress reduction coefficient for liquefaction |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_shear\_stress\_reduction\_coefficient\_\_youd2001liquefaction}(z) \\ \hspace{1em} r_d \gets \frac{1 - 0.4113 z^{0.5} + 0.04052 z + 0.001753 z^{1.5}}{1 - 0.4177 z^{0.5} + 0.05729 z - 0.006205 z^{1.5} + 0.00121 z^{2}} \\ \hspace{1em} r_d \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( r_d, 0, 1 \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ r_d \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
shear_stress_reduction_coefficient |
float
|
Shear stress reduction coefficient for liquefaction |
get_shear_stress_reduction_factor__baez1993advances(
stone_column_arrangement,
area_replacement_ratio=float("nan"),
shear_modulus_ratio=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_shear\_stress\_reduction\_factor\_\_baez1993advances}(\mathrm{stone\_column\_arrangement}, A_r, G_r) \\ \hspace{1em} \mathbf{if} \ \lnot \mathrm{stone\_column\_arrangement} \\ \hspace{2em} \mathbf{return} \ \mathrm{float} \mathopen{}\left( \textrm{"nan"} \mathclose{}\right) \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} K_G \gets \frac{1}{1 + A_r \cdot \mathopen{}\left( G_r - 1 \mathclose{}\right)} \\ \hspace{1em} \mathbf{return} \ K_G \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
stone_column_arrangement
|
str
|
Arrangement of stone columns |
required |
area_replacement_ratio
|
float
|
Ratio of one column area to the unit cell area |
float('nan')
|
shear_modulus_ratio
|
float
|
Ratio of stone column to soil shear modulus |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
shear_stress_reduction_factor |
float
|
Shear stress reduction factor for stone columns |
get_stone_column_is_present(
depth,
stone_column_arrangement,
stone_column_top_depth=float("nan"),
stone_column_bottom_depth=float("nan"),
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_stone\_column\_is\_present}(z, \mathrm{stone\_column\_arrangement}, z_{top}, z_{bottom}) \\ \hspace{1em} \mathbf{if} \ \lnot \mathrm{stone\_column\_arrangement} \\ \hspace{2em} \mathbf{return} \ \mathrm{np}.\mathrm{full\_like} \mathopen{}\left( z, \mathrm{False} \mathclose{}\right) \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ \mathopen{}\left( z \ge z_{top} \mathclose{}\right) \mathbin{\&} \mathopen{}\left( z \le z_{bottom} \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
stone_column_arrangement
|
str
|
Arrangement of stone columns |
required |
stone_column_top_depth
|
float
|
Top depth of stone column |
float('nan')
|
stone_column_bottom_depth
|
float
|
Bottom depth of stone column |
float('nan')
|
Returns:
| Name | Type | Description |
|---|---|---|
stone_column_is_present |
bool
|
Indicates presence of stone column |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_thickness\_liquefiable\_layer}(FS_{liq}, H) \\ \hspace{1em} \textrm{" calculated as the total thickness of liquefiable sand layers "} \\ \hspace{1em} H \gets \mathrm{np}.\mathrm{broadcast\_to} \mathopen{}\left( H, FS_{liq}.\mathrm{shape} \mathclose{}\right) \\ \hspace{1em} H_2 \gets \mathrm{np}.\mathrm{copy} \mathopen{}\left( H \mathclose{}\right) \\ \hspace{1em} \mathrm{np}.\mathrm{putmask} \mathopen{}\left( H_2, \mathord{\sim} \mathopen{}\left( FS_{liq} \le 1 \mathclose{}\right), 0 \mathclose{}\right) \\ \hspace{1em} H_2 \gets \sum H_2 \\ \hspace{1em} \mathbf{return} \ H_2 \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
thickness
|
float
|
Thickness of soil layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
thickness_liquefiable_layer |
float
|
Thickness of liquefiable sand layer |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_thickness\_non\_liquefiable\_layer}(FS_{liq}, z) \\ \hspace{1em} \textrm{" calculated as the total thickness above the first liquefiable sand layer "} \\ \hspace{1em} H_1 \gets \mathopen{}\left[ \mathclose{}\right] \\ \hspace{1em} \mathbf{for} \ \mathrm{fs\_liq} \in \mathrm{np}.\mathrm{atleast\_2d} \mathopen{}\left( FS_{liq} \mathclose{}\right) \ \mathbf{do} \\ \hspace{2em} \mathrm{flag} \gets \mathrm{fs\_liq} \le 1 \\ \hspace{2em} \mathbf{if} \ \mathrm{np}.\mathrm{any} \mathopen{}\left( \mathrm{flag} \mathclose{}\right) \\ \hspace{3em} a \gets \mathrm{flag}.\mathrm{argmax} \mathopen{}\left( \mathclose{}\right) \\ \hspace{3em} \mathrm{z\_surface\_layer} \gets \left\{ \begin{array}{ll} \mathrm{depth}_{a - 1}, & \mathrm{if} \ a > 0 \\ 0, & \mathrm{otherwise} \end{array} \right. \\ \hspace{2em} \mathbf{else} \\ \hspace{3em} \mathrm{z\_surface\_layer} \gets \mathrm{np}.\mathrm{inf} \\ \hspace{2em} \mathbf{end \ if} \\ \hspace{2em} H_1.\mathrm{append} \mathopen{}\left( \mathrm{z\_surface\_layer} \mathclose{}\right) \\ \hspace{1em} \mathbf{end \ for} \\ \hspace{1em} \mathbf{if} \ FS_{liq}.\mathrm{ndim} < 2 \\ \hspace{2em} H_1 \gets \mathrm{thickness\_non\_liquefiable\_layer}_{0} \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ H_1 \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
thickness_non_liquefiable_layer |
float
|
Thickness of non-liquefiable surface layer |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_triaxial\_planes\_correction}() \\ \hspace{1em} K_r \gets 1.0 \\ \hspace{1em} \mathbf{return} \ K_r \\ \mathbf{end \ function} \end{array}
\]
Args:
Returns:
| Name | Type | Description |
|---|---|---|
triaxial_planes_correction |
float
|
Correction for shearing of incorrect planes in cyclic triaxial test |
get_volumetric_strain__cetin2009probabilisticb(
clean_sand_normalized_blow_count,
volumetric_strain_depth_weighting_factor,
liquefaction_safety_factor,
cyclic_stress_ratio_ss_20_1d_1atm,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_volumetric\_strain\_\_cetin2009probabilisticb}(N_{160cs}, DF, FS_{liq}, CSR_{SS,20,1D,1atm}) \\ \hspace{1em} CSR_{SS,20,1D,1atm} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( CSR_{SS,20,1D,1atm}, 0.05, 0.6 \mathclose{}\right) \\ \hspace{1em} N_{160cs} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( N_{160cs}, 5, 40 \mathclose{}\right) \\ \hspace{1em} ε_v \gets 1.879 \log \mathopen{}\left( \frac{780.416 \log CSR_{SS,20,1D,1atm} - N_{160cs} + 2442.465}{636.613 N_{160cs} + 306.732} \mathclose{}\right) + 5.583 \\ \hspace{1em} ε_v \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( FS_{liq} \ge 2, 0, ε_v \mathclose{}\right) \\ \hspace{1em} ε_v \gets ε_v \cdot DF \\ \hspace{1em} \mathrm{calibration\_coefficient} \gets 1.15 \\ \hspace{1em} ε_v \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( ε_v, 0, \mathrm{None} \mathclose{}\right) \\ \hspace{1em} ε_v \gets \mathrm{calibration\_coefficient} \cdot \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( ε_v \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ ε_v \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
clean_sand_normalized_blow_count
|
float
|
Equivalent clean sand SPT blow count (N_160) |
required |
volumetric_strain_depth_weighting_factor
|
float
|
Depth weighting factor for volumetric strain |
required |
liquefaction_safety_factor
|
float
|
Factor of safety against liquefaction triggering |
required |
cyclic_stress_ratio_ss_20_1d_1atm
|
float
|
CSR value corresponding to a 1 dimensional, 20 uniform loading cycles simple shear test under a confinement pressure of 1 atm |
required |
Returns:
| Name | Type | Description |
|---|---|---|
volumetric_strain |
float
|
Volumetric strain in soil |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_volumetric\_strain\_depth\_weighting\_factor\_\_cetin2009probabilisticb}(z) \\ \hspace{1em} DF \gets \mathopen{}\left| 1 - \frac{z}{18} \mathclose{}\right| \\ \hspace{1em} \mathbf{return} \ DF \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
depth
|
float
|
Depth below ground surface to bottom of layer |
required |
Returns:
| Name | Type | Description |
|---|---|---|
volumetric_strain_depth_weighting_factor |
float
|
Depth weighting factor for volumetric strain |
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_volumetric\_strain\_spt\_\_idriss2008soil}(γ_{max}, N_{160cs}) \\ \hspace{1em} γ_{max} \gets \mathrm{np}.\mathrm{clip} \mathopen{}\left( γ_{max}, \mathrm{None}, 100 \cdot 0.08 \mathclose{}\right) \\ \hspace{1em} ε_v \gets 1.5 \exp \mathopen{}\left( -0.369 \sqrt{ N_{160cs} } \mathclose{}\right) γ_{max} \\ \hspace{1em} ε_v \gets \mathrm{np}.\mathrm{nan\_to\_num} \mathopen{}\left( ε_v \mathclose{}\right) \\ \hspace{1em} \mathbf{return} \ ε_v \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
max_shear_strain
|
float
|
Maximum shear strain in soil |
required |
clean_sand_normalized_blow_count
|
float
|
Equivalent clean sand SPT blow count (N_160) |
required |
Returns:
| Name | Type | Description |
|---|---|---|
volumetric_strain |
float
|
Volumetric strain in soil |
get_youd2002revised_t15_parameters(
is_t15_liquefiable_layers,
fines_content,
diameter_at_50_percent_finer,
thickness,
lateral_spread_displacement_as_scalar=False,
)
Calculation function.
\[
\begin{array}{l} \mathbf{function} \ \mathrm{get\_youd2002revised\_t15\_parameters}(T_{15\ flag}, FC, D_{50}, H, LD_{scalar}) \\ \hspace{1em} \mathbf{if} \ \mathrm{np}.\mathrm{any} \mathopen{}\left( \mathrm{np}.\mathrm{isnan} \mathopen{}\left( \mathrm{np}.\mathrm{extract} \mathopen{}\left( T_{15\ flag}, D_{50} \mathclose{}\right) \mathclose{}\right) \mathclose{}\right) \\ \hspace{2em} \mathrm{raise\_value\_error} \mathopen{}\left( \textrm{"null diameter\_at\_50\_percent\_finer values at is\_t15\_liquefiable\_layers, check inputs"} \mathclose{}\right) \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} T_{15} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( T_{15\ flag}, H, \mathrm{np}.\mathrm{nan} \mathclose{}\right) \\ \hspace{1em} \mathbf{if} \ LD_{scalar} \\ \hspace{2em} T_{15} \gets \mathrm{np}.\mathrm{nansum} \mathopen{}\left( T_{15} \mathclose{}\right) \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} FC_{T15} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( T_{15\ flag}, FC, \mathrm{np}.\mathrm{nan} \mathclose{}\right) \\ \hspace{1em} \mathbf{if} \ LD_{scalar} \\ \hspace{2em} FC_{T15} \gets \mathrm{np}.\mathrm{nanmean} \mathopen{}\left( FC_{T15} \mathclose{}\right) \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} D_{50T15} \gets \mathrm{np}.\mathrm{where} \mathopen{}\left( T_{15\ flag}, D_{50}, \mathrm{np}.\mathrm{nan} \mathclose{}\right) \\ \hspace{1em} \mathbf{if} \ LD_{scalar} \\ \hspace{2em} D_{50T15} \gets \mathrm{np}.\mathrm{nanmean} \mathopen{}\left( D_{50T15} \mathclose{}\right) \\ \hspace{1em} \mathbf{end \ if} \\ \hspace{1em} \mathbf{return} \ \mathopen{}\left( T_{15}, FC_{T15}, D_{50T15} \mathclose{}\right) \\ \mathbf{end \ function} \end{array}
\]
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
is_t15_liquefiable_layers
|
bool
|
Liquefiable layers with N_160 < 15 |
required |
fines_content
|
float
|
Percentage of fines passing No. 200 sieve |
required |
diameter_at_50_percent_finer
|
float
|
Diameter at 50% finer from sieve analysis |
required |
thickness
|
float
|
Thickness of soil layer |
required |
lateral_spread_displacement_as_scalar
|
bool
|
If disabled, calculates lateral displacement for each depth |
False
|
Returns:
| Name | Type | Description |
|---|---|---|
cumulative_thickness_liquefiable_layers |
float
|
Cumulative thickness of saturated granular layers with N_160 < 15 |
fines_content_liquefiable_layers |
float
|
Average fines content for liquefiable layers within T_15 |
diameter_at_50_percent_finer_liquefiable_layers |
float
|
Average mean grain size for liquefiable layers within T_15 |