Settlement

class groundhog.shallowfoundations.settlement.SettlementCalculation(soilprofile)

Calculates shallow foundation settlement under a certain distributed load

calculate(**kwargs)

Calculates the consolidation settlement using the specified grid, foundation shape and loading

calculate_foundation_stress(applied_stress, offset=0, poissonsratio=0.3, **kwargs)

Calculates the vertical stress increase below the foundation. By default, the calculation happens below the center of the foundation (offset=0). The Boussinesq solution for the selected foundation shape is used.

calculate_initial_state(waterlevel, specific_gravity=2.65, unitweight_water=10.0, **kwargs)

Calculates the initial stress distribution and void ratio. The water level needs to be set for every calculation (z-axis positive downward).

calculate_mv(**kwargs)

Calculates the consolidation settlement using the specified grid, foundation shape and loading. Instead of using the compression index and recompression index, the modulus of volumetric compressibility \(m_v\) is used.

create_grid(dz=0.5, custom_nodes=None, **kwargs)

Creates a grid for calculation

plot_initial_state(plot_title='', e0_range=(0, 3), fillcolordict={'CLAY': 'brown', 'SAND': 'yellow'}, **kwargs)

Plots the initial stress vs depth and the initial void ratio vs depth

plot_result(plot_title='', fillcolordict={'CLAY': 'brown', 'SAND': 'yellow'}, **kwargs)

Plots the settlement resulting from the stress increase

plot_stress_increase(plot_title='', fillcolordict={'CLAY': 'brown', 'SAND': 'yellow'}, **kwargs)

Plots the initial stress vs depth and the stress increase

set_foundation(width, shape='strip', length=nan, skirt_depth=0)

Sets the size and shape of the foundation. Length only needs to be defined when shape='rectangular'.

TODO: When a skirt depth is defined, the stress increase is transferred to the base of the skirts. Compression of the soil inside the skirt is then not taken into account.

Parameters:

• width – Width of the foundation (diameter for circular foundations) [m]

• shape – Shape of the foundation: 'strip' (default), 'circular' or 'rectangular'

• length – Out-of-plane length (only required for a rectangular foundation)

• skirt_depth – Depth of skirts [m]. The skirts are assumed to transfer the load to the base level of the skirts

groundhog.shallowfoundations.settlement.consolidationsettlement_mv(initial_height, effective_stress_increase, compressibility, **kwargs)

Calculates the consolidation settlement using the compressibility \(m_v\) (inverse of constrained modulus \(M\)).

The constrained modulus is stress-dependent and therefore the relation between \(M\) and \(C_c\) is also stress-dependent.

Parameters:

• initial_height – Initial thickness of the layer (\(H_0\)) [\(m\)] - Suggested range: initial_height >= 0.0

• effective_stress_increase – Increase in vertical effective stress under the given load (\(\Delta sigma_{v}^{\prime}\)) [\(kPa\)] - Suggested range: effective_stress_increase >= 0.0

• compressibility – Modulus of volumetric compressibility derived from oedometer tests (\(m_v\)) [\(-\)] - Suggested range: 1e-4 <= compressibility <= 10 (note that the compressibility is stress-dependent)

\[ \begin{align}\begin{aligned}\Delta \epsilon = m_v \cdot \Delta \sigma_v^{\prime}\\\Delta z = \Delta \epsilon \cdot H_0\\m_v = \frac{C_c}{2.3 \cdot (1 + e_0) \cdot \sigma_{v0}^{\prime}}\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys:

• ’delta z [m]’: Consolidation settlement (\(\Delta z\)) [\(m\)]

• ’delta epsilon [-]’: Change in strain caused by consolidation (\(\delta \epsilon\)) [\(-\)]

Reference - Budhu (2011). Soil mechanics and foundation engineering

groundhog.shallowfoundations.settlement.primaryconsolidationsettlement_nc(initial_height, initial_voidratio, initial_effective_stress, effective_stress_increase, compression_index, e_min=0.3, **kwargs)

Calculates the primary consolidation settlement for normally consolidated fine grained soil.

Parameters:

• initial_height – Initial thickness of the layer (\(H_0\)) [\(m\)] - Suggested range: initial_height >= 0.0

• initial_voidratio – Initial void ratio of the layer (\(e_0\)) [\(-\)] - Suggested range: 0.1 <= initial_voidratio <= 5.0

• initial_effective_stress – Initial vertical effective stress in the center of the layer (\(\sigma_{v0}^{\prime}\)) [\(kPa\)] - Suggested range: initial_effective_stress >= 0.0

• effective_stress_increase – Increase in vertical effective stress under the given load (\(\Delta sigma_{v}^{\prime}\)) [\(kPa\)] - Suggested range: effective_stress_increase >= 0.0

• compression_index – Compression index derived from oedometer tests (\(C_c\)) [\(-\)] - Suggested range: 0.1 <= compression_index <= 0.8 (derived using logarithm with base 10)

• e_min – Minimum void ratio below which no further consolidation occurs (\(e_{min}\)) [\(-\)] - Default=0.3

\[ \begin{align}\begin{aligned}\Delta z = \frac{H_0}{1 + e_0} C_c \log_{10} \frac{\sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime}}{\sigma_{v0}^{\prime}}\\\Delta e = C_c \log_{10} \frac{\sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime}}{\sigma_{v0}^{\prime}}\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys:

• ’delta z [m]’: Primary consolidation settlement for normally consolidated soil (\(\Delta z\)) [\(m\)]

• ’delta e [-]’: Decrease in void ratio for the normally consolidated soil (\(\delta e\)) [\(-\)]

• ’e final [-]’: Final void ratio after consolidation (:math:` e_{final}`) [\(-\)]

Reference - Budhu (2011). Soil mechanics and foundation engineering

groundhog.shallowfoundations.settlement.primaryconsolidationsettlement_oc(initial_height, initial_voidratio, initial_effective_stress, preconsolidation_pressure, effective_stress_increase, compression_index, recompression_index, e_min=0.3, **kwargs)

Calculates the primary consolidation settlement for an overconsolidated clay. This material is characterised using a compression index and a recompression index which can be derived from oedometer tests.

The settlement depends on whether the stress increase loads the layer beyond the preconsolidation pressure. If stresses remain below the preconsolidation pressure, the recompression index applies. If stresses go beyond the preconsolidation pressure, the compression index will apply for the increase beyond the preconsolidation pressure.

Note that a minimum void ratio is set to prevent calculated void ratios from dropping below the minimum.

Parameters:

• initial_height – Initial thickness of the layer (\(H_0\)) [\(m\)] - Suggested range: initial_height >= 0.0

• initial_voidratio – Initial void ratio of the layer (\(e_0\)) [\(-\)] - Suggested range: 0.1 <= initial_voidratio <= 5.0

• initial_effective_stress – Initial vertical effective stress in the center of the layer (\(\sigma_{v0)^{\prime}\)) [\(kPa\)] - Suggested range: initial_effective_stress >= 0.0

• preconsolidation_pressure – Preconsolidation pressure, maximum vertical stress to which the layer has been subjected (\(p_c^{\prime}\)) [\(kPa\)] - Suggested range: preconsolidation_pressure >= 0.0

• effective_stress_increase – Increase in vertical effective stress under the given load (\(\Delta sigma_{v}^{\prime}\)) [\(kPa\)] - Suggested range: effective_stress_increase >= 0.0

• compression_index – Compression index derived from oedometer tests (\(C_c\)) [\(-\)] - Suggested range: 0.1 <= compression_index <= 0.8

• recompression_index – Recompression index derived from the unloading step in oedometer tests (\(C_r\)) [\(-\)] - Suggested range: 0.015 <= recompression_index <= 0.35

• e_min – Minimum void ratio below which no further consolidation occurs (\(e_{min}\)) [\(-\)] - Default=0.3

\[ \begin{align}\begin{aligned}\Delta z = \frac{H_0}{1 + e_0} C_r \log_{10} \frac{\sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime}}{\sigma_{v0}^{\prime}}; \ \sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime} < p_c^{\prime}\\\Delta z = \frac{H_0}{1 + e_0} \left( C_r \log_{10} \frac{p_c^{\prime}}{\sigma_{v0}^{\prime}} + C_c \log_{10} \frac{\sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime}}{p_c^{\prime}} \right); \ \sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime} > p_c^{\prime}\\\Delta e = C_r \log_{10} \frac{\sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime}}{\sigma_{v0}^{\prime}}; \ \sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime} < p_c^{\prime}\\\Delta e = C_r \log_{10} \frac{p_c^{\prime}}{\sigma_{v0}^{\prime}} + C_c \log_{10} \frac{\sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime}}{p_c^{\prime}} ; \ \sigma_{v0}^{\prime} + \Delta \sigma_v^{\prime} > p_c^{\prime}\end{aligned}\end{align} \]

Returns:

Dictionary with the following keys:

• ’delta z [m]’: Primary consolidation settlement for the overconsolidated soil (\(\delta z\)) [\(m\)]

• ’delta e [-]’: Decrease in void ratio for the overconsolidated soil (\(\delta e\)) [\(-\)]

• ’e final [-]’: Final void ratio after consolidation (:math:` e_{final}`) [\(-\)]

Cases for calculating the primary consolidation settlement

Reference - Budhu (2011). Soil mechanics and foundation engineering

class groundhog.shallowfoundations.settlement.SettlementCalculation(soilprofile)

Calculates shallow foundation settlement under a certain distributed load

__init__(soilprofile)

Initializes the settlement calculation with a certain SoilProfile object. The SoilProfile object is checked for the presence of the required columns: ('Total unit weight [kN/m3]', 'Cc [-]', 'Cr [-]', 'OCR [-]'). Optionally, a column with the saturation S [-] can be defined (ranging from 0 to 1). If a saturation is defined, it will be taken into account for the calculation of the void ratio.

calculate(**kwargs)

Calculates the consolidation settlement using the specified grid, foundation shape and loading

calculate_foundation_stress(applied_stress, offset=0, poissonsratio=0.3, **kwargs)

Calculates the vertical stress increase below the foundation. By default, the calculation happens below the center of the foundation (offset=0). The Boussinesq solution for the selected foundation shape is used.

calculate_initial_state(waterlevel, specific_gravity=2.65, unitweight_water=10.0, **kwargs)

Calculates the initial stress distribution and void ratio. The water level needs to be set for every calculation (z-axis positive downward).

calculate_mv(**kwargs)

Calculates the consolidation settlement using the specified grid, foundation shape and loading. Instead of using the compression index and recompression index, the modulus of volumetric compressibility \(m_v\) is used.

create_grid(dz=0.5, custom_nodes=None, **kwargs)

Creates a grid for calculation

plot_initial_state(plot_title='', e0_range=(0, 3), fillcolordict={'CLAY': 'brown', 'SAND': 'yellow'}, **kwargs)

Plots the initial stress vs depth and the initial void ratio vs depth

plot_result(plot_title='', fillcolordict={'CLAY': 'brown', 'SAND': 'yellow'}, **kwargs)

Plots the settlement resulting from the stress increase

plot_stress_increase(plot_title='', fillcolordict={'CLAY': 'brown', 'SAND': 'yellow'}, **kwargs)

Plots the initial stress vs depth and the stress increase

set_foundation(width, shape='strip', length=nan, skirt_depth=0)

Sets the size and shape of the foundation. Length only needs to be defined when shape='rectangular'.

TODO: When a skirt depth is defined, the stress increase is transferred to the base of the skirts. Compression of the soil inside the skirt is then not taken into account.

Parameters:

• width – Width of the foundation (diameter for circular foundations) [m]

• shape – Shape of the foundation: 'strip' (default), 'circular' or 'rectangular'

• length – Out-of-plane length (only required for a rectangular foundation)

• skirt_depth – Depth of skirts [m]. The skirts are assumed to transfer the load to the base level of the skirts