Classic Theory
Convergence analysis of excavation and calculation of the maximum settlement in a homogeneous body are the same for all classic theories. The subsidence trough analyses then differ depending on the assumed theory (Peck, Fazekas, Limanov).
When calculating settlement the program first determines the radial load of a circular excavation as:
where: | σz | - | geostatic stress in the center of the 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 the vicinity of the excavation | |
ν | - | Poisson's ratio of rock/soil in the vicinity of the 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 the vicinity of the excavation | |
ν | - | Poisson's number of rock/soil in the vicinity of the 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 the vicinity of the excavation |