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Vertical Bearing Capacity - Spring Method

The program module "Pile - spring method" is part of the "Pile" program. It allows to calculate the pile vertical bearing capacity in general layered subsoil. This analysis provides the load-settlement curve and distributions of forces and displacements developed along the pile.

The main advantage of this module is availability of the required input parameters of soils around the pile - the user is asked to specify the angle of internal friction, cohesion, unit weight and deformation modulus of a given soil.

The solution procedure in the module "Pile - spring method" is based on a semi-analytical approach. The response of soil surrounding the pile follows from the well known solution of layered subsoil as a generalization of the Winkler-Pasternak model. The elastic rigid plastic response in shear is assumed along the pile-soil interface in view of the Mohr-Coulomb failure criterion. The normal stress acting on the pile is determined from the geostatic stress and soil (concrete mixture) pressure at rest.

The influence of water in the vicinity of pile is not only introduced into the shear bearing capacity of the pile skin, but also affects the depth of influence zone below the pile heel. 

Providing the pile reaches incompressible subsoil the spring method cannot be used.

The pile settlement can also be influenced by the settlement of the surrounding terrain. In particular, settlement of soil may reduce the pile bearing capacity. The pile settlement increases without increasing load. This phenomenon is modeled in the program as so called negative skin friction.

The analysis may also account for the influence of technological process of pile construction on the stiffness of pile foundation.

The solution procedure consists of several steps:


In analysis the pile subdivided into a number of segments. Subdivision into individual segments complies with the condition that the ratio between the pile segment and its diameter should be approximately equal to 2.5. The minimum number of segments is 10.


Each segment is in the analysis characterized by a spring. The spring stiffness serves to model both the shear resistance of skin and at the pile heel the stiffness of soil below the pile heel.


For each segment the limit value of shear force Tlim transmitted by the skin is determined.


The pile is loaded at its top end by increments of the vertical load. For each load increment the magnitude of spring force for each segment is determined. However, it cannot exceed the limit value of skin friction Tlim. It is clear that for a certain load level all springs will no longer be able to increase their force and with additional load increase the pile becomes supported by the base spring only. This spring has no restriction on the transmitted force.


As a result the analysis provides the load-settlement curve, forces developed in the pile and a graph showing variation of shear as a function of deformation at a given location.