Analysis of Cusp Catastrophic Model for Vertical Stability of Drilling Shaft Lining

Abstract

The vertical stability analysis of the drilling shaft lining has long been a technical problem in the construction of underground space development projects. And the critical depth of vertical stability was a key parameter to judge its stability. To determine this parameter, a simple and practical computational method would be helpful. In this paper, a new vertical stability analysis model of shaft lining structure based on catastrophe theory was proposed. In accordance with the mechanical analysis, the catastrophic instability mechanics was analyzed and a new critical depth of drilling shaft lining was deduced. Further, the rationality and feasibility of the catastrophic calculation model was proved by the numerical simulation results in a case. And the sensitivity of the influencing parameters was also analyzed, which provided theoretic reference for optimization design and guiding security construction. The results implied that catastrophic calculation model, as an alternative method for shaft stability analysis, could be applied to theoretical analysis and guiding engineering practice in the study of drilling shaft lining’s vertical stability.

Study on the Vertical Stability of Drilling Wellbore under Optimized Constraints

“…It has been seen from Figure 3 that the structure is in an unstable state when m ≤ 0, which means that the points appear inside the bifurcation points set B. For Equation (22), when ∆ = 0, it has two identical roots out of three roots, which is the critical state for the system to mutate. When ∆ > 0, it has only one real root and two complex roots, at which time we consider the system to be stable.…”

“…In this part, several representative drilling wellbore projects were selected, and the critical depth values before and after using optimization measures were calculated. The critical depth before adopting optimization measures was calculated based on reference [23]. The critical depth after adopting optimization measures was calculated by the Equation (36) in this article.…”

“…The critical depth before adopting optimization measures was calculated based on reference [23]. The critical depth after adopting optimization measures was calculated by the Equation (36) in this article. The selected representative projects included the Panji west wind wellbore, the Keke gai coal mine wind wellbore, the Banji coal mine auxiliary wellbore, and the Banji coal mine main wellbore.…”

“…Cheng et al [21] further established the critical depth of the variable cross-section drilling wellbore structure. Liu et al [22,23] established the critical depth of the equal cross-section drilling wellbore structure using catastrophe theory considering the sudden and irreversible characteristics of the wellbore instability process. Rong et al [24] used numerical calculation methods to analyze the vertical stability of the entire drilling process.…”

Numerical Modeling on Blasting Stress Wave in Interbedding Rheological Rockmass for the Stability of the Main Shaft of Mine

“…In Reference (Chen et al, 2010), a three-dimensional finite element model was established to analyze the force and deformation characteristics of the wall rock of a long and large vertical shaft lined with supporting concrete based on the ideal elastoplastic material constitutive relationship and the Drucker-Prager yield principle. In Reference (Liu et al, 2020), the criteria for vertical shaft stability and the limit depth expression were derived to investigate the effects of differences in tension-compression strength of rock and intermediate principal stress on the limit depth of a vertical shaft. In Reference (Xie et al, 2019), The finite element method was used to perform numerical simulation of the effects of dynamic excavation of roadways in the middle section and large chambers in Jinchuan No.…”