Nonlinear soil spring

The non-linear soil spring is a line support for 1D members. It is intended to model soil reaction using real soil parameters.

The model consist of six springs, four of then are acting perpendicular to the member axis and are used to model the soil loading and stiffness at the top, bottom, left and right side of the beam.

The two remaining springs are used to model friction in translation along the local x-axis and rotation around the local x-axis.

The nonlinear soil spring can be used in a nonlinear or nonlinear staged analysis.

$image\NonlinearSoilSpring.gif$

Description of spring types which can be connected at the line support

In each position 6 spring are connected, 4 translation springs acting perpendicular to the local x axis (i.e. springs z+, z-, y + and y -), one translation spring acting in local x and one spring Rx acting in rotation around the local x axis.

At Z+ and Z- side, three different functions types are allowed:
- Type A, i.e. linear soil function with plastic braches at its begin end at its end , for modelling of non-consolidated soil,
- Type B, i.e. bi-linear soil function with plastic braches at its begin end at its end, for modelling of consolidated soil,
- Type C, i.e. water function, hyper elastic type, for Archimedes law.
At Y+ and Y- side, two different functions types are allowed:

- Type A, i.e. linear soil function with plastic braches at its begin end at its end , for modelling of non-consolidated soil,
- Type B, i.e. bi-linear soil function with plastic braches at its begin end at its end, for modelling of consolidated soil.
At X, a function with a linear part and a horizontal branch connected at its end. The height of the plastic yielding is equal to the total reaction of spring A or B multiplied by the friction coefficient. Spring type C (water spring) does not effect the friction.

At Rx, a function with a linear part and a horizontal branch connected at its end. The height of the plastic yielding is equal to the total reaction multiplied with his friction coefficient

The non-linear soil spring can be used in a non-linear staged analysis. Unloading is supported.

Hyper elastic unloading, i.e. the same path as during the loading is followed during unloading, even if the plastic yielding occurred.

Plastic unloading, i.e. in unloading, the linear, bi-linear branch (for type A or type B) is taken immediately.

Type A and B can have hyper elastic or plastic unloading.

Type C, i.e. water function, area is always of hyper elastic type, for Archimedes law.

Function type A

U0	Gap [mm]
Qa	Active pressure [kN/m]
Qn	Neutral pressure [kN/m]
Qp	Passive pressure [kN/m]
C1	Soil stiffness [kN/m˛]
C2	Soil stiffness [kN/m˛]

$image\ebx_1719663894.gif$

Elastic

$image\NonlinSoilSpringAElastic.gif$

Plastic

$image\NonlinSoilSpringAPlastic.gif$

Function type B

U0	Gap [mm]
Qa	Active pressure [kN/m]
Qn	Neutral pressure [kN/m]
Qc	Consollidation pressure [kN/m]
Qp	Passive pressure [kN/m]
C1	Soil stiffness [kN/m˛]
C2	Soil stiffness [kN/m˛]

Elastic

$image\NonlinSoilSpringBElastic.gif$

Plastic

$image\NonlinSoilSpringBPlastic.gif$

Function type C

The function is used to model water reaction on a diving or sinking member. Bellow picture and description of the parameters.

Elastic unloading is always applied.

U0	Gap [mm]
Qp	Maximal water pressure [kN/m]
C1	Stiffness [kN/m]

$image\NonlinSoilSpringC.gif$

This function based on the law of Archimedes. When the member starts at water level 0m and submerges, the acting force is proportional to the volume below the water surface.

The water spring is of type "Hyper elastic". It means that no losses occur due to unloading. The path of loading is the same as the path of unloading.

This function can be connected at Z+ and at Z- side of the pipeline support.

Friction

The function is connected at X and Rx parameters and is used to model friction.

Bi-linear springs with the maximum (plastic behaviour) depending on the pressure force.

$image\NonlinSoilSpringFriction.gif$

Cfriction represents the elasticity of the spring and is together with the plastic friction force the only property of the spring.

The program computes interaction between the friction spring caused by torsion and by a normal force. The type of friction interaction is circular. The interaction implies that the maximum value of 'normal' axial friction spring is reduced by the interaction between axial forces and torsion.

Torsion squared + Axial force squared = 1

The procedure to input a new nonlinear soil spring

Open service Structure.
Start function Model data >Support > nonlinear soil spring.
Type and adjust the parameters of the support (see below).
Confirm with [OK].
Input the support into the model.
Close the function.
Close the service.

Required project functionality

In the Project setup dialogue, the following functionality must be switched ON if the nonlinear soil spring is to defined:

Nonlinearity > Support nonlinearity / Soil spring,
Nonlinearity > Friction support / Soil spring.