### Objective:

One of the biggest problems encountered when building numerical models for layers is the lack of exact deterministic material parameters. Therefore, stochastic models should be use. However, these models have the general drawback of overusing computer resources. This project developed a stochastic model with the ability to use a shear modulus in conjunction with a special iteration scheme allowing efficient implementation.

### Method:

With the Karhunen Loeve Expansion (KLE), it is possible to split the stochastic shear modulus, and therefore the whole system, into a deterministic and a stochastic part. These parts can then be transformed into a linear system of equations using finite elements and Chaos Polynomial Decomposition. Combining the KLE and the Fourier Transformation in combination with Plancherel's theorem enables decoupling of the deterministic part into smaller subsystems. An iteration scheme was developed which narrows the application of "costly" routines to only these smaller deterministic subsystems, instead of the whole higher dimensional (up to a dimension of 10,000) system matrix.

### Application:

As concerns about vibrations produced by machinery and traffic have increased in past years, models that can predict vibrations in soil became more important. However, since material parameters for soil layers cannot be measured exactly in practice, it is reasonable to use stochastic models.