It is often necessary to estimate the potential ground surface settlement caused by underground infrastructure projects involving tunnels and underbores. Such settlement assessments are used to determine if any additional protection works are necessary particularly if underbores are tunnels are to be constructed underneath roads, railways or buildings. Finite element analysis programs such as Plaxis 2D/3D, Optum G2/G3 or FLAC are typically used to model settlements in such instances. Accurate information on ground properties, tunnel parameters and loading conditions is required to provide accurate settlement assessments.
In situations where a quick estimate with minimum data inputs is required, a common semi-empirical method developed by Peck (1969) is also commonly used. This method is based on field observations made by Peck, and the ground settlement trough profile is approximated by a Gaussian distribution curve. The volume loss in the tunnel (overbreak or annular collapse) is equated to the area under the Gaussian curve from which a settlement profile is generated. The width of the settlement trough varies between soil types and is controlled by a parameter (Kg) that is specified for different soil types and strengths. I developed a web application (https://underbore-settlement.anvil.app/), also embedded below, to estimate settlements based on the Gaussian curve method developed by Peck.
It should be noted that since this method does not consider any volume change in soils (consolidation or dilation), it is valid only as an initial estimate under short-term conditions.
The figure below shows results from the above method compared to the results from a simple Plaxis 2D model. A tunnel with 1m diameter and 2m of cover subject to a volume loss of 10% bored through undrained soft clay and loose sand was modelled separately in Plaxis 2D to compare against the results using Peck's method with recommended numbers for Kg, for clay (0.5) and sand (0.3) respectively.
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| Comparison between Plaxis output and Gaussian curve method by Peck (1969) |
It can be seen that the results from Plaxis and Gaussian curve method are similar for sand, but varies slightly for clay. Using a Kg value of 0.7 for clay leads to a curve very similar to the Plaxis 2D output. The choice of Kg for various soil types with different strengths is a subject of research, and available literature suggests that a Kg value of 0.4-0.7 is appropriate for soft clays. However, with an understanding of the limitations of the Gaussian curve method, it can be used as a rough initial estimate of settlements before embarking on detailed finite element analysis. The web application linked above will be useful for such quick assessments.
