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Ground Loss
Classical theory
Convergence analysis of an excavation and calculation of the maximum settlement in a homogeneous body are the same for all classical theories. The subsidence trough analyses then differ depending on the assumed theory (Peck, Fazekas, Limanov).
When calculating settlement the program first determines the radial loading of a circular excavation as:
| where: | σz | - | geostatic stress in center of excavation |
| Kr | - | coefficient of pressure at rest of cohesive soil |
The roof ua and the bottom ub deformations of excavation follow from:
| where: | Z | - | depth of center point of excavation |
| r | - | excavation radius | |
| E | - | modulus of elasticity of rock/soil in vicinity of excavation | |
| ν | - | Poisson's number of rock/soil in vicinity of excavation |
The maximum terrain settlement and the length of subsidence trough are determined as follows:
| where: | Z | - | depth of center point of excavation |
| r | - | excavation radius | |
| E | - | modulus of elasticity of rock/soil in vicinity of excavation | |
| ν | - | Poisson's number of rock/soil in vicinity of excavation |
When the tunnel roof displacement is prescribed the maximum settlement is provided by the following expression:
| where: | Z | - | depth of center point of excavation |
| r | - | excavation radius | |
| ua | - | tunnel roof displacement | |
| ν | - | Poisson's number of rock/soil in vicinity of excavation |
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