Excursus: Compressibility

This section provides a brief summary of the moduli used to describe the compressibility - elastic modulus, deformation modulus, and stiffness modulus - of the soil and shows the mathematical relationship between these values.

The moduli differ among other things in the type of determination, in particular through the implementation of the boundary conditions for the lateral expansion.

Modulus of Elasticity E

The modulus of elasticity is a material constant which, according to HOOKE, can be obtained from the uniaxial compression test (i.e. with a uniaxial stress state). The side stretching is made possible unhindered.

Stiffness modulus E_s/E_oed

The stiffness modulus is among others depends on the tension level and is obtained from the compression test (Ödometer according to TERZAGHI). The lateral stretching is prevented, so that a uniaxial stretching condition prevails. It is also known as the oedometric module.

Deformation modulus E_v

The deformation modulus is among others depends on the stress level and is obtained in situ from the plate load test. Side stretching is only partially hindered.

The mentioned moduli can be converted into one another depending on the stress level if the Poisson's ratio ν is known. The following relationship exists, which can be traced in the literature, for example, in Refer [1 ].

E_{s} = E \cdot \frac{1 - ν}{(1 + ν) \cdot (1 - 2 ν)}

E_{v} = E \cdot \frac{1}{(}

\Rightarrow E_{v} = E_{s} \cdot \frac{(1 + ν) \cdot (1 - 2 ν)}{(1 - ν) \cdot (1 - ν^{2})}

Relation Between Elastic Modulus, Stiffness Modulus, and Defomation Modulus of Soil

In general:

E_{s} > E_{v} > E

Relation of Material Parameters of Soil Compressibility

References

Hartmann, K. A.: Untersuchung zur Prognose von Anforderungswerten an die Beschleunigungsmesswerte der FDVK – Methode. Lehrstuhl und Prüfamt für Grundbau, Bodenmechanik und Felsmechanik der Technischen Universität München. Schriftenreihe Heft 34. München. 2002

Parent section

Material models