On characterizing spatially variable soil shear strength using spatial average

• We compare the actual response of a spatially variable soil mass with its spatial average response.
• The above comparison is done for soil column, retaining wall, and shallow foundation.
• Spatial average response is close to actual response only if the critical slip curve is constrained.
• Spatial average response is not close to actual response if the critical slip curve is not constrained.

The purpose of this study is to examine in more detail under what conditions would spatial averaging over some prescribed region be sufficient to reproduce the response statistics arising from a spatially variable field. The spatially variable undrained shear strength is first simulated by a random field, and the actual response of a spatially variable clay in three problems (soil column, retaining wall, shallow foundation) is simulated using the random finite element method. This actual response is then compared to the spatial average response (the response of a homogeneous clay whose undrained shear strength is equal to certain spatial average). It is observed that the actual response can be well approximated by the spatial average response only for situations where the critical slip curve is constrained. This constraint is the most significant for the retaining wall and the least significant for the soil column.