A Combined Analytical and Numerical Approach for the Evaluation of Radial Loads on the Lining of Vertical Shafts

Abstract

The evaluation of the load acting on a shaft support is of fundamental importance for the correct dimensioning of the structure. The load acting on the support can appear somewhat complex. One approach may be to use the convergence-confinement method (CCM) normally used in the tunneling design. This process involves intersecting the convergenceconfinement (CC) curve with the support reaction line. However, in order to be able to adopt this technique, it is necessary to know the radial displacement of the shaft wall at the point in which the support is to be installed. Using the equations of Vlachopoulos and Diederichs (2009) the reaction line of the support can be calculated. Numerical models developed with Flac 2D v.6.0 considering the Mohr-Coulomb criterion and an ideal elastic-plastic behavior simulating stepwise excavation and support installation were developed. The relation between applied internal stress and radial displacement of the wall shaft, obtained by the numerical simulation was compared with the CC curve obtained by the CCM and it showed a good match between the two methods. However, an iterative procedure has also been used to insert the reaction line in the CC graph. The result shows lower initial displacements (and therefore greater radial stress) when compared with the values obtained by numerical calculation with the axisymmetric model. It is therefore recommended the combined use of the CCM (analytical method) and the axisymmetric numerical model (step by step simulation) to obtain the values of the final load on the lining and the final plastic radius, necessary for the correct design of supporting structures on the shaft wall.

Estimation of Shaft Radial Displacement beyond the Excavation Bottom before Installation of Permanent Lining in Nondilatant Weak Rocks with a Novel Formulation

“…By means of the CCC, the design iterative procedure can be quicker. Based on recent numerical analysis (Oreste et al2016), the use of the CCC method combined the equations of Vlachoupulos and Diederichs (2009), in order to define the starting point of the reaction line, leads to a non-exact evaluation of the final pressure acting on the lining (Oreste et al 2016). The equations of Vlachoupulos and Diederichs ( 2009), originally obtained in absence of supporting structure, cannot be used for positioning in a reliable way the reaction line on the CCC of the shaft.…”

“…The excavation step was chosen as 1.2m, since it was possible to observe its marginal influence on the final results (see Oreste et al 2016). The excavation phase and support installation were considered as simultaneous, i.e.…”

Verification and Comparison of Direct Calculation Method for the Analysis of Support–Ground Interaction of a Circular Tunnel Excavation

“…Therefore, this curve determines when the support is installed and the stiffness of the support plays an important role [14][15][16][17]. Numerous studies have been investigating this approach, using empirical and mathematical expressions to develop GRCs under different behavioral assumptions and generally applicable to tunnels excavated in isotropic stress state [18][19][20][21]. The curve DEI denotes the SCC that characterizes the deformation imposed on the support and its ability to withstand the radially converging pressure (point D) that has occurred since the support was installed.…”

“…The curve DEI denotes the SCC that characterizes the deformation imposed on the support and its ability to withstand the radially converging pressure (point D) that has occurred since the support was installed. There are many studies on SCC that focus on the transient conditions of supports, progressive hardening, time-dependent properties, and non-linearities [5,6,15,19,[22][23][24]. Numerous studies have explored the analytical solutions of SCC and GRC at equilibrium (point E) under different hypotheses [25][26][27][28].…”

“…2022, 12, x FOR PEER REVIEW 2 of 13 support was installed. There are many studies on SCC that focus on the transient conditions of supports, progressive hardening, time-dependent properties, and non-linearities [5,6,15,19,[22][23][24]. Numerous studies have explored the analytical solutions of SCC and GRC at equilibrium (point E) under different hypotheses [25][26][27][28].…”