This paper deals with the loading and deforma-tion of the tunnel cross section perpendicular to the longitudinal axis during the construction phase of a tunnel in shield dri-ving in the context of annular gap filling with liquid mortar. Since in some cases damage to the lining segments is de-tected which occurs early after a ring has been constructed, there is a technical and economic motivation for a better un-derstanding of the internal stresses in the tunnel in the longitudinal direction of the tunnel during the construction phase. The aim of the present work is to develop a coherent calculation method to consider this situation on the basis of analytical approaches and to identify, describe and quantify relevant aspects which influence the loading of the tunnel during the construction phase. In the present work, analytical approaches are used for the most part to ensure a continuous, comprehen-sible and transparent calculation method. © 2022, VDI Fachmedien GmBH & Co. KG. All rights reserved.

Describing rock strength under true triaxial conditions with the limit condition of Mogi-Coulomb. It is known that investigations of rock strength under true triaxial conditions can show the influence of the mean principal stress on failure. For numerical calculations of tunnels and boreholes, where the mean and minimum principal stresses are not identical, limit conditions that take into account the influence of the mean principal stress would be advantageous. With the limit condition according to Mogi-Coulomb, unlike with the well-known limit condition according to Mohr-Coulomb, the influence of the mean principal stress can be taken into account. At the same time, however, these two limit conditions are identical for triaxial extension and compression. In order to be able to map limit states even more appropriate, the modified limit condition according to Mogi-Coulomb is presented in this article. In this modified form, the limit conditions according to Drucker-Prager and von Mises are included as a special case. In order to understand the Mogi-Coulomb criterion and to show possible applications, the present article shows its form, the influence of the parameters, the convexity and parameter acquisition of laboratory tests are examined. , Ernst und Sohn. All rights reserved.

Describing rock strength under true triaxial conditions with the limit condition of Mogi-Coulomb. It is known that investigations of rock strength under true triaxial conditions can show the influence of the mean principal stress on failure. For numerical calculations of tunnels and boreholes, where the mean and minimum principal stresses are not identical, limit conditions that take into account the influence of the mean principal stress would be advantageous. With the limit condition according to Mogi-Coulomb, unlike with the well-known limit condition according to Mohr-Coulomb, the influence of the mean principal stress can be taken into account. At the same time, however, these two limit conditions are identical for triaxial extension and compression. In order to be able to map limit states even more appropriate, the modified limit condition according to Mogi-Coulomb is presented in this article. In this modified form, the limit conditions according to Drucker-Prager and von Mises are included as a special case. In order to understand the Mogi-Coulomb criterion and to show possible applications, the present article shows its form, the influence of the parameters, the convexity and parameter acquisition of laboratory tests are examined. © 2021, Ernst und Sohn. All rights reserved.

Analytical approximate solution for ground water flow at a residual water drainage system. If excavations are conducted which go below the groundwater table, it makes sense to embed the pit wall in a less permeable soil stratum and to operate a residual water drainage system. With such a construction water flows under the pit walls and so a flow field arises which has to be determined for various calculations and stability verifications. For instance, hydraulic gradients, discharge velocities as well as potential heads and pore-water pressures have to be calculated. These values are needed to determine the earth and water pressure distribution. They can also be used for verifications in relation to hydraulic failure, internal erosion and failure of the earth support, and also for the calculation of groundwater influx. Using the Finite Element Method (FEM) a systematic parameter study is conducted as the basis for formulating analytical approximation solutions, including theoretical boundary cases. It is possible to optimize the parametric study for both plane and axis-symmetrical states with isotropic and anisotropic subsoil and to do this by defining the hydraulic problem as a parameterized boundary value problem. By evaluating the mathematical characteristics of the boundary value problem and conducting a dimensional analysis it is possible to reduce the number of parameters considerably. Copyright © 2017 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin

Application of an approximate solution for groundwater flow at a residual water drainage system. If excavations go below the groundwater table, a proven option is to embed the pit wall in a less permeable soil stratum and to operate a residual water drainage system. As an underflow of the pit walls occurs in these constructions the flow field has to be determined for various calculations and stability verifications. For instance, hydraulic gradients, discharge velocities as well as potential heads and pore-water pressures have to be calculated. These values are necessary to determine the earth and water pressure distribution. They can also be used for the verification of hydraulic failure, internal erosion and failure of the earth support, as well as for the calculation of groundwater influx. By defining the hydraulic problem as a parameterized boundary value problem and using the Finite Element Method (FEM) an analytical approximate solution was formulated. This solution is valid for both plane and axisymmetric state with isotropic and anisotropic subsoil. It is used for the calculation of the hydraulic head distribution on the level of the wall toe and along the inner surface of the wall. These approximate solutions are evaluated for the verification against hydraulic heave and for the calculation of the maximum gradient at the change of layer in area of the excavation pit and the determination of the required embedment depth. Copyright © 2016 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin

It is rational, in excavations in the subsoil beneath the groundwater table, to embed the pit wall in a less permeable soil stratum and operate a residual-water drainage system. The Finite Element Method (FEM) can be used to determine both the influx of groundwater and the potentials and pore-water pressures relevant for various analyses of stability. Such numerical calculations require the selection of a model size and the assumption of certain boundary conditions, however. The influence of these on the results of the calculation are examined in this paper. A study has been performed for the cases of plane and axis-symmetrical states with isotropic and anisotropic subsoil, and is firstly optimised by formulating the task as a parameterised boundary value problem. Evaluation of the mathematical characteristics of the boundary value problem and dimensional analysis are then used to reduce the number of parameters. Finally, conclusions concerning the necessary model size and boundary conditions are drawn on the basis of the parameter study, and recommendations then provided for the user. Copyright © 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin.

In this article calculations for two exemplary systems of excavation pit walls are performed using the Finite Element Method (FEM). The first system represents a single anchored pit wall, the second a double supported pit wall. For both systems the calculated earth pressures and the pressures of the earth support are evaluated as well as the bending moments of the wall, the supporting forces, the displacements of the wall and finally the overall stability. In the study the friction angle of the soil and the excavation level are varied. As a first goal the influence of the friction angle on the calculated results are presented which are relevant for design of the structure. Based on this parameter study it will be shown how the different design approaches according to Eurocode 7 influence the design. For example, the effect of reduction of the friction angle according to design approach DA3 is compared with an increase of the internal forces according to DA2. Also discussed are different ways to reduce the friction angle with FEM to proof the overall stability. Finally, conclusions are drawn to the application of the FEM in different proofs of stability of excavation pit walls and hints are given to model the elements of the construction. © 2015 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin.