Modulus of subsoil reaction derived from iterations

The program allows for automatic calculation of the modulus of subsoil reaction from deformational characteristics of soil from iteration process. The procedure builds on the assumption that deformation of the elastic subspace characterized by the deformation modulus Edef [MPa] when changing the stress state associated with the change of earth pressures is the same as deformation of the underground wall.

The goal therefore is to find such values of k_h [MN/m³] so that the continuity of deformations of wall and adjacent soil is maintained. Plastic deformation of structure is not considered when performing analysis with k_h iteration.  This approach is schematically cleared by computing the modulus of subsoil reaction of the i^th segment of wall free of anchor, see figure:

Determination of modulus of subsoil reaction of i^th segment

For change of stress σ_r -σ the program determines uniform loading σ_ol [MPa] of individual segments of a structure. Next, the overall change of stress passing the i^th segment (σ_i*l [MPa*m]) is computed. This change is caused by additional loading of the soil body due to segments 1 to n (σ_ol,1 - σ_ol,n). The overall change of stress Δσ_i is reduced by structural strength m_iσ_or,i [MPa]. The new value of the spring stiffness then follows from: 

where:	Edef	-	deformation modulus of elastic subspace
	σol	-	uniform load applied to segments of structure
	σil	-	overall change of stress behind ith segment of structure

The change of stress inside the soil body is determined according to Boussinesque. Inserting the new value of k directly into the next calculation would cause instable iteration – therefore the value of k that is introduced into the next analysis of the wall is determined from the original value of k_p and the new value of k_n of the modulus of subsoil reaction.

where:	kp	-	original value of modulus of subsoil reaction
	kn	-	new value of modulus of subsoil reaction

Maximum modulus of the subsoil reaction of the i^th layer is limited by the value:

where:

Edef,i

-

deformation modulus of ith layer

The iterative procedure used when computing the modulus of subsoil reaction is as follows:

1) Determine the matrix of influence values for deriving change of stress in a depth of the soil body passing the i^th segment of a structure due to surcharge caused by the change of stress in other segments.

2) The first approximation of the modulus k_h in front of the wall is introduced – a triangular distribution of values at the wall heel k_h = 10 MN/m³ is assumed.

3) Perform analysis of the wall.

4) Compute new values of k_h and determine new values for the next analysis.

5) The dialog window to check the iteration appears and the program waits till the next command. If the next n iterations are selected, the steps 3 and 4 are repeated n–times to arrive again at the step No. 5. The analysis is terminated in this dialog window by pressing the "Stop" button.

This iterative process is controlled by the user – he or she has to decide whether the results make sense.