# Negative skin friction¶

groundhog.deepfoundations.axialcapacity.negativeskinfriction.negativeskinfriction_pilegroup_zeevaertdebeer(depths, effective_unit_weights, lateral_earth_pressure_coefficients, interface_friction_angles, surcharge, diameter, diameter_influence, **kwargs)[source]

Calculates the negative skin friction for a pile in a pile group according to the method of Zeevaert en De Beer. To allow any unit weight profile, the differential equation is solved in finite difference form.

Parameters
• depths – Array with depths used for the calculation ($$z$$) [$$m$$] - Elementtype: float, order: ascending, unique: True, empty entries allowed: False

• effective_unit_weights – Array with effective unit weights used for the calculation ($$\gamma^{\prime}$$) [$$kN/m3$$] - Elementtype: float, order: None, unique: False, empty entries allowed: False

• lateral_earth_pressure_coefficients – Array with lateral earth pressure coefficient at each depth ($$K_0$$) [$$-$$] - Elementtype: float, order: None, unique: False, empty entries allowed: False

• interface_friction_angles – Array with interface friction angles ($$\delta^{\prime}$$) [$$deg$$] - Elementtype: float, order: None, unique: False, empty entries allowed: False

• surcharge – Amount of stress applied on top of the soil mass ($$p_0^{\prime}$$) [$$kPa$$] - Suggested range: surcharge >= 0.0

• diameter – Pile diameter ($$D_p$$) [$$m$$] - Suggested range: 0.01 <= diameter <= 10.0

• diameter_influence – Diameter of the zone of influence for negative skin friction ($$D_n$$) [$$m$$] - Suggested range: diameter_influence >= 0.0

\begin{align}\begin{aligned}\frac{d \sigma_v^{\prime}}{dz} = \gamma^{\prime} - \tau \cdot \frac{O_s}{A}\\m = K_0 \cdot \tan \delta^{\prime} \cdot \frac{O_s}{A}\\\frac{\Delta \sigma_{v,i+1}^{\prime}}{\Delta z} - \gamma^{\prime} + m \cdot \sigma_{v,i}^{\prime} = 0\\\sigma_{v,0}^{\prime} = p_0^{\prime}\\O_s = \pi \cdot D_p\\A = \frac{\pi}{4} \cdot \left( D_n^2 - D_p^2 \right)\end{aligned}\end{align}
Returns

Dictionary with the following keys:

• ’virgin_effective_stress [kPa]’: Effective stress profile in the absence of surcharge ($$\sigma_{vo}^{\prime}$$) [$$kPa$$]

• ’group_effective_stress [kPa]’: Effective stress accounting for the effect of soil hanging on the pile ($$\sigma_{v}^{\prime}$$) [$$kPa$$]

• ’negative_skin_friction_profile_single [kN]’: Cumulative negative skin friction for a single pile ($$F_{n}$$) [$$kN$$]

• ’negative_skin_friction_profile_group [kN]’: Cumulative negative skin friction for pile in the group ($$F_{n, group}$$) [$$kN$$]

• ’negative_skin_friction [kN]’: Total value of negative skin friction for a single pile ($$F_{n,tot}$$) [$$kN$$]

• ’negative_skin_friction_group [kN]’: Total value of negative skin friction for a pile in a group ($$F_{n,tot,group}$$) [$$kN$$]

Pile group with contributing soil and equilibrium of infinitesimal soil slice

Reference - Zeevaert - De Beer (1966)