A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes

Abstract

Summary This paper generalizes the finite strain Coulomb solution of Vrakas and Anagnostou (Int J Numer Anal Meth Geomech 2014; 38(11): 1131–1148) for the classic tunnel mechanics problem of the ground response curve to elastoplastic grounds satisfying a non‐linear Mohr's failure criterion. A linear (Coulomb‐type) plastic potential function is used, leading to a non‐associated flow law, and edge plastic flow is considered in the plastic zone. The solution for a general non‐linear Mohr's failure criterion is semi‐analytical in that it requires the evaluation of definite integrals. In the special case of the Hoek–Brown criterion, however, these integrals are calculated analytically, resulting in a rigorous closed‐form series solution. The applicability of the derived solution is illustrated through the example of the Yacambú‐Quibor tunnel, where very large deformations were observed when crossing of weak graphitic phyllites. Copyright © 2016 John Wiley & Sons, Ltd.

Elastoplastic Analysis of Circular Openings in Elasto‐Brittle‐Plastic Rock Mass Based on Logarithmic Strain

“…However, (13) denotes that the elastic parameters influence the rock mass stress distribution form, and this is the main difference from the solutions based on the classic SS theory.…”

“…For the elastic rock mass, the stress can be theoretically obtained with Runge-Kutta method with the boundary conditions of (7) by combining the differential equations of (11) and (13). However, the boundary conditions are only formulated by radial stress at = and → ∞, and the plastic radius is still unknown.…”

“…In order to obtain the solutions, the values of plastic radius and stress state ( 0 , ) at = 1000 0 are given. Then, the stresses can be recursively calculated from 1000 0 to by (11) and (13). If the calculated stress at = satisfies the peak yield criterion of (4a), the solutions would be correct.…”

“…Moreover, when Young's modulus is significantly small, the calculated displacement may be larger than the excavation radius, which is in conflict with the real condition. In view of this fact, logarithmic strain is employed to predict the tunnel contraction displacement with similarity methods for perfect elastoplastic rock mass [12][13][14]. Unfortunately, the rock-like material generally manifests brittle failure behavior once its peak strength is reached.…”

Mohr–Coulomb plasticity for sands incorporating density effects without parameter calibration

“…The Mohr–Coulomb plasticity model is also widely used in research work, since it allows one to capture the pressure‐dependent strength of a geomaterial with a fraction of costs for sophisticated constitutive models. This exceptional efficiency makes the model a common choice for computationally intensive simulations in geomechanics, such as those involve complex domains, soil‐structure interactions, contacts, large deformations, and/or coupled multiphysics …”