Effective Young’s modulus for a three-dimensional spatially variable elementary soil mass

In order to simplify the geotechnical problems, engineers usually assumed the soil to be homogeneous. However, the soil was formed naturally with complicated processes, it should not be homogeneous. If we have to use a value to represent its property, how to determine this value? This study focus on the Young’s modulus. We use random finite element analysis to simulate a soil mass with spatially variable Young’s modulus subjected to displacement-controlled 1D compression and back-calculate the overall Young’s modulus by the stress responses. Define the overall Young’s modulus as the effective Young’s modulus(Eeff). We investigate whether the effective Young’s modulus can be strongly correlated to any spatial average. For the 3D elementary soil mass problems, we find that the numerical vales and statistics of effective Young’s modulus can be approximated by appropriate spatial averages. For isotropic cases, Eeff can be approximated by geometric mean. For layer cases, Eeff can be approximated by arithmetic mean (Ea) when loading direction is parallel to the layers and can be approximated by harmonic mean (Eg) when loading direction is perpendicular to the layers. For column cases, Eeff can be approximated by harmonic mean(Eh) when loading direction is parallel to the columns and can be approximated by geometric mean when loading direction is perpendicular to the columns. And the unified spatial average model can approximate Eeff in every case above without switch among Ea, Eg and Eh. Fenton and Griffiths (2002, 2005) studied probabilistic foundation settlement, and they found that for foundations on soils with isotropic SOFs, Eeff can be modeled as Eg of the E random field over a prescribed domain under the footing. For elementary soil mass problems, we have the consistent and more stronger results. We find that not only the statistics but also the numerical values of Eeff can be approximated by appropriate apatial averages. However, when we go back to foundation problems, we find only the statistics of Eeff can be approximated by apatial averages. The reason why the results of elementary soil mass can’t be applied on the foundation problems needs more investigation.