Berechnung von Winkler-Pasternak-Konstanten aus Verformungsparametern von Böden
Im Programm werden die Winkler-Pasternak-Konstanten C1 und C2 aus der Gleichheitsbedingung der Matrizen der Biegsamkeit eines unendlich festen unendlichen Streifenfundaments berechnet, der auf dem Winkler-Pasternak-Untergrund und auf der elastischen Schicht ruht.
Diese Bedingung ist in den folgenden Gleichungen dargestellt:
Edef | - | deformation modulus [MPa] |
ν | - | Poisson's ratio |
Eoed | - | oedometric modulus [MPa] |
G | - | shear modulus [MPa] |
Of these, Edef and ν are independent, the other two are determined by relations:
and
The strip footing has a width of 2b and the deformation zone under the strip has a thickness of H.
By the solution of the elastic subgrade we mean finding the relationship between the displacement and the load of the strip footing in the form:
where P is the flexibility matrix.
By solving for an isotropic homogeneous elastic layer under the foundation waist while avoiding horizontal displacements, we obtain a flexibility matrix P of the form:
where
and
By solving the differential equation for the two-parameter subsoil model, we obtain a matrix P of the form:
where C1, C2 are the constants of the Winkler-Pasternak subsoil model. We find their values from the condition that the matrix P of expression (4) must be identical to the matrix P of expression (7). By comparison and modification we obtain the relations:
and
where
and
From relations (8) and (9), the values of C1 and C2, are directly calculated, while the infinite sums in expressions (10) and (11) are performed in Geo5 for the first 21 addends.
Literature: Kuklík, P.: Příspěvek k řešení vrstevnatého podloží, Pozemní stavby, 7-1984