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

Abstract

The Convergence-Confinement Method (CCM) applies to circular tunnels in an in situ stress field in which all three principal stresses are equal and where the rock mass exhibits elastoperfectly plastic shear failure. As the radial wall displacement cannot be easily obtained by using analytical methods, an extensive parametric analysis of the bi-dimensional numerical modelling in order to investigate the strain of the shaft wall close to the excavation bottom was performed. 81 cases were derived from the combination of the geometrical parameters and three weak rock categories. By processing the data relating to u R0 (radial displacement of the shaft wall at the excavation bottom) values obtained by numerical calculation in the different cases studied, it was possible to calculate the u R0 /R ratio as a function of the lithostatic stress p 0 , the lining thickness s, and the shaft radius R. Novel equations were obtained for quickly estimating the value of u R0 knowing the lining concrete thickness, the shaft depth and the shaft radius, for the different qualities of rock considered.

Design Study of Steel Fibre Reinforced Concrete Shaft Lining for Swelling Ground in Toronto, Canada

“…The Fast Lagrangian Analysis of Continua (FLAC) 2D, two-dimensional continuum explicit finite element analysis code developed by Itasca consulting group Inc., was used. This software has been widely used for geotechnical analysis application in the fields of civil mining engineering [56][57][58].…”

Evaluating the Impact of Blast‐Induced Damage on the Rock Load Supported by Liner in Construction of a Deep Shaft: A Case Study of Ventilation Shaft of Micangshan Road Tunnel Project

“…When the convergence confinement method (CCM) is used to estimate the radial loads on the shaft lining, the relationship of the radial ground displacement, U R , and the equivalent internal pressure acting on the rock mass, P i , need to be obtained first. is relationship is represented by the convergenceconfinement curve (CCC), which is important for the analysis of the interaction between the rocks and the shaft lining [25,26]. e CCC of the rocks around the shaft was calculated using the following sequence in the aforementioned numerical model: (i) initiate the model with zero displacement and initial in situ stress, including gravitational loading; (ii) null the shaft elements to be excavated and insert the BDZ after the excavation face passed each section to simulate the damage of rock mass, the extent of the BDZ in numerical analysis was determined based on the result of seismic survey; (iii) apply radial pressure to the excavation surface.…”

“…Taking the intersection between the convergence-confinement curve (CCC) and the reaction line of the support into account, Spagnoli et al [25] proposed new equations for estimation of radial loads on the shaft lining. Combining the CCM and numerical analysis, Spagnoli et al [26] investigated the relationship between the radial loads acting on liner support and the radial displacement of the ground for vertical circular shaft sinking in weak rocks, and they concluded that the lining thickness would affect the radial loads and radial ground displacement. e ground displacement around a deep shaft in highly stressed ground largely depends on the mechanical properties of the rock mass [27].…”